Finite Automata

We show there is a unique maximal positive variety of languages which does not contain the language (ab) * . This variety is the unique maximal positive variety satisfying the two following conditions: it is strictly included in the class of rational languages and is closed under the shuffle operation. It is also the largest proper positive variety closed under length preserving morphisms. The ordered monoids of the corresponding variety of ordered monoids are characterized as follows: for every pair (a, b) of mutually inverse elements, and for every element z of the minimal ideal of the submonoid generated by a and b, (abzab) ω ≤ ab. In particular this variety is decidable.

We propose a simple and intuitive algorithm for solving md-DFA problem using algorithm concepts within extended operators, our approach shows quadratic polynomial time and hence proves the equivalence between polynomial and non-polynomial classes, we have also shown that minimal nonemptiness of automata problem can be solved in polynomial time with help of modified subset construction, rather that building a product automaton, which lead to factorial size of the memory and time, in this work we also have used many non-tractable existing examples and computed them in polynomial time, which guarantees that our algorithm solves NP-complete problem in almost linear polynomial time, we have also avoided the problem of product automata by an algorithmic approach, we are also giving the starting ground for the proof of back-reference problem which was discussed before, notion to the globally local increment is also given as the main argument towards the resolution of "P versus NP" theorem, which coincides with the finitarity term in general mathematics.

We are to investigate the most common mistake in science and failure, which goes through the lenses of what is to be done and proved, thus, we give the full proof in this book according to “P versus NP” theorem by Stephen Cook, which was speculated as the way of what could be solved also can be verified – which is a common misinterpretation as we give the definition of tractability and feasibility of the non-solvable problems like NP-complete when the solution can be found only passing through the whole space of available variants – the number of these entities together form “too big” numbers which are not countable and are at least exponential as 2n. The classical NP-complete problem is a problem of Traveling Salesman Problem (TSP) by Hamilton, which shows that for n-cities there at least n! (factorial) number of possible solutions which are to be verified and, according to the verification procedure or step, they are to be chosen for the optimal one or the tour with the smallest possible function f(x), for each x that forms the path from the solution space.

One of the unresolved problems faced in the construction of intelligent tutoring systems is the acquisition of background knowledge, either for the specification of the teaching strategy, or for the construction of the student model, identifying the deviations of students' behavior. In this paper, we argue that the use of sequential pattern mining and constraint relaxations can be used to automatically acquire that knowledge. We show that the methodology of constrained pattern mining used can solve this problem in a way that is difficult to achieve with other approaches.

The thesis aims at a further study on semi-flower automata – the concept introduced by Giambruno and Restivo to study finitely generated submonoids of free monoids. The material of the thesis is an interplay between automata and algebraic structures. In fact, using semi-flower automata we study the intersection problem of submonoids of free monoids. Further, we study certain structural properties of semi-flower automata using algebraic structures. Contributing to the intersection problem of submonoids of free monoids, in this thesis, we obtain a sufficient condition for the Hanna Neumann property of the submonoids which are generated by finite prefix sets of words. In this connection, we obtain a general rank formula for the submonoids accepted by SFA. In order to study structural properties of semi-flower automata, we choose to study holonomy decomposition and on syntactic complexity. We ascertain holonomy decomposition and syntactic complexity of certain subclasses of circular sem...

We present a new criterion for proving that a language is not multiple contextfree, which we call a Substitution Lemma. We apply it to show a sample selection of languages are not multiple context-free, including the word problem of F 2 × F 2. Our result is in contrast to Kanazawa et al. [2014, Theory Comput. Syst.] who proved that it was not possible to generalise the standard pumping lemma for context-free languages to multiple context-free languages, and Kanazawa [2019, Inform. and Comput.] who showed a weak variant of generalised Ogden's lemma does not apply to multiple context-free languages. We also show that groups with multiple context-free word problem have decidable rational subset membership and intersection problems.

The minimal deterministic finite automaton is generally used to determine regular languages equality. Using Brzozowski's notion of derivative, Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp proposed an almost linear algorithm for testing the equivalence of two deterministic finite automata that avoids minimisation. In this paper we improve this algorithm's best-case running time, present an extension to non-deterministic finite automata, and establish a relationship with the one proposed in Almeida et al., for which we also exhibit an exponential lower bound. We also present some experimental comparative results.

We propose a productivity-based account of vagueness. Predicates remain bivalent over the intended universe, but their extensions may be productive, explaining the persistence of borderline cases as a structural failure of effective decidability rather than a semantic gap. We distinguish contrary (term) negation from complementary negation and prove that, for sharp predicates, term negation coincides with logical/complementary negation. We further show an effective obstruction: no effectively enumerable family of precisifications, each providing a c.e. approximation, can capture a productive extension; a uniform escape operator always produces counterexamples. The model yields a dynamic, one‑sided account of vagueness that improves on supervaluationist, fuzzy, and rough‑set approaches by explaining the perpetual emergence of new borderline cases without appealing to a predicate–complement partition.

Regular expressions provide a flexible means for matching strings and they are often used in dataintensive applications. They are formally equivalent to either deterministic finite automata (DFAs) or nondeterministic finite automata (NFAs). Both DFAs and NFAs are affected by two problems known as amnesia and acalculia, and DFAs are also affected by a problem known as insomnia. Existing techniques require an automata conversion and compaction step that prevents the use of existing automaton databases and hinders the maintenance of the resulting compact automata. In this paper, we propose Parallel Finite State Machines (PFSMs), which are able to run any DFAor NFA-like state machines without a previous conversion or compaction step. PFSMs report, online, all the matches found within an input string and they solve the three aforementioned problems. Parallel Finite State Machines require quadratic time and linear memory and they are distributable. Parallel Finite State Machines make very fast distributed regular expression matching in data-intensive applications feasible.

ABSTV, ACT. A method is presented for computing upper bounds for the speedup gamed by synchronousmultiprocessor, bottom-up, no-backtrack parsing of strings generated by a context-free grammar. First the maxunum speedup s is defined using an optimal strategy for a certain pebble game Then analyuc upper and lower bounds for s are developed These bounds are computed for parsing trees with certain propertms. The computation consists of (1) determining a subclass of strings of a language which are favorably parsed in parallel, (2) estabhshing sets of difference equations and solving them to estimate the minimum time needed to parse these strings; and (3) computing the speedup function. The method is applied to the parsing of arithmetic expressions and strings of a stmple programming language. The results presented show how maxtmum speedup gums vary with the number of processors avadable.

In many fields, such as language acquisition, neuropsychology of language, the study of ageing, and historical linguistics, corpora are used for estimating the diversity of grammatical structures that are produced during a period by an individual, community, or type of speakers. In these cases, treebanks are taken as representative samples of the syntactic structures that might be encountered. Generalizing the potential syntactic diversity from the structures documented in a small corpus requires careful extrapolation whose accuracy is constrained by the limited size of representative sub-corpora. In this article, I demonstrate—both theoretically and empirically—that a grammar’s derivational entropy and the mean length of the utterances (MLU) it generates are fundamentally linked, giving rise to a new measure, the derivational entropy rate. The mean length of utterances becomes the most practical index of syntactic complexity; I demonstrate that MLU is not a mere proxy, but a fundamental measure of syntactic diversity. In combination with the new derivational entropy rate measure, it provides a theory-free assessment of grammatical complexity. The derivational entropy rate indexes the rate at which different grammatical annotation frameworks determine the grammatical complexity of treebanks. I evaluate the Smoothed Induced Treebank Entropy (SITE) as a tool for estimating these measures accurately, even from very small treebanks. I conclude by discussing important implications of these results for both NLP and human language processing.

Journal Article by Dr Fermín Moscoso del Prado Martín published in Computational Linguistics, presented by Suchir Salhan at ACL 2025, Vienna Austria.

In this paper, a reflection is made on an indeterminism inherent to Hopcroft's minimization algorithm: the splitter choice. We have implemented two natural policies (FIFO and FILO) for managing the set of splitters for which we obtain the following practical results: the FILO strategy performs better than the FIFO strategy, in the case of a one letter alphabet, the practical complexity in the FILO case never exceeds a linear one and our implementation is more efficient than the minimization algorithm of the FSM tool. This implementation is being integrated in a finite automata library, the Dash library. Thus, we present an efficient manner to manipulate automata by using canonical minimal automata.

In this paper, we present an algorithm that can be used to convert phi into a solvable form. This is done using binary combinations and the relations between them. Binary combinations are all 2-Clauses that can be obtained from n literal of phi and with their help we convert phi into a readable form phi_2 . phi_1 and phi_2 are equivalent (phi_1 is the same as orginal phi), so we can solve phi_2 instead of solving phi_1 .The algorithm performs the transform operation in 4 steps , and in each step it converts phi_i to phi_i+1. phi_i s and phi are equivalent. It can be proven that in the worst case phi_5 is solvable. The time and space order of this algorithm is O(n^96) .

A cellular automaton (CA) is a parallel synchronous computing model, which consists in a juxtaposition of finite automata (cells) whose state evolves according to that of their neighbors. Its trace is the set of infinite words representing the sequence of states taken by some particular cell. In this paper we study the ultimate trace of CA and partial CA (a CA restricted to a particular subshift). The ultimate trace is the trace observed after a long time run of the CA. We give sufficient conditions for a set of infinite words to be the trace of some CA and prove the undecidability of all properties over traces that are stable by ultimate coincidence.

The verification of monadic second-order (MSO) graph properties, equivalently, the model-checking problem for MSO logic over finite binary relational structures, is fixed-parameter tractable (FPT) for the parameter consisting of the formula that expresses the property and the tree-width or the clique-width of the input graph or structure. How to build usable algorithms for this problem ? The proof of the general theorem (an algorithmic meta-theorem, cf. ) is based on the description of the inputs by algebraic terms and the construction of finite automata that accepts the terms describing the satisfying inputs. But these automata are in practice much too large to be constructed . A typical number of states is 2 2 10 and lower-bounds match this number. Can one use automata and overcome this difficulty ? We propose to use fly-automata (FA) . They are automata whose states are described and not listed, and whose transitions are computed on the fly and not tabulated. When running on a term of size 1000, a fly-automaton with 2 2 10 states computes only 1000 transitions if it is deterministic. FA can have infinitely many states. For example, a state can record, among other things, the (unbounded)

Some recent results have introduced external-memory algorithms to compute self-indexes of a set of strings, mainly via computing the Burrows-Wheeler Transform (BWT) of the input strings. The motivations for those results stem from Bioinformatics, where a large number of short strings (called reads) are routinely produced and analyzed. In that field, a fundamental problem is to assemble a genome from a large set of much shorter samples extracted from the unknown genome. The approaches that are currently used to tackle this problem are memory-intensive. This fact does not bode well with the ongoing increase in the availability of genomic data. A data structure that is used in genome assembly is the string graph, where vertices correspond to samples and arcs represent two overlapping samples. In this paper we address an open problem of : to design an external-memory algorithm to compute the string graph.

A mobile agent (robot), modeled as a finite automaton, has to visit all nodes of a regular graph. How does the memory size of the agent (the number of states of the automaton) influence its exploration capability? In particular, does every increase of the memory size enable an agent to explore more graphs? We give a partial answer to this problem by showing that a strict gain of the exploration power can be obtained by a polynomial increase of the number of states. We also show that, for automata with few states, the increase of memory by even one state results in the capability of exploring more graphs.

ADVERTIMENT. L'accés als continguts d'aquesta tesi doctoral i la seva utilització ha de respectar els drets de la persona autora. Pot ser utilitzada per a consulta o estudi personal, així com en activitats o materials d'investigació i docència en els termes establerts a l'art. 32 del Text Refós de la Llei de Propietat Intel•lectual (RDL 1/1996). Per altres utilitzacions es requereix l'autorització prèvia i expressa de la persona autora. En qualsevol cas, en la utilització dels seus continguts caldrà indicar de forma clara el nom i cognoms de la persona autora i el títol de la tesi doctoral. No s'autoritza la seva reproducció o altres formes d'explotació efectuades amb finalitats de lucre ni la seva comunicació pública des d'un lloc aliè al servei TDX. Tampoc s'autoritza la presentació del seu contingut en una finestra o marc aliè a TDX (framing). Aquesta reserva de drets afecta tant als continguts de la tesi com als seus resums i índexs. ADVERTENCIA. El acceso a los contenidos de esta tesis doctoral y su utilización debe respetar los derechos de la persona autora. Puede ser utilizada para consulta o estudio personal, así como en actividades o materiales de investigación y docencia en los términos establecidos en el art. 32 del Texto Refundido de la Ley de Propiedad Intelectual (RDL 1/1996). Para otros usos se requiere la autorización previa y expresa de la persona autora. En cualquier caso, en la utilización de sus contenidos se deberá indicar de forma clara el nombre y apellidos de la persona autora y el título de la tesis doctoral. No se autoriza su reproducción u otras formas de explotación efectuadas con fines lucrativos ni su comunicación pública desde un sitio ajeno al servicio TDR. Tampoco se autoriza la presentación de su contenido en una ventana o marco ajeno a TDR (framing). Esta reserva de derechos afecta tanto al contenido de la tesis como a sus resúmenes e índices. WARNING. Access to the contents of this doctoral thesis and its use must respect the rights of the author. It can be used for reference or private study, as well as research and learning activities or materials in the terms established by the 32nd article of the Spanish Consolidated Copyright Act (RDL 1/1996). Express and previous authorization of the author is required for any other uses. In any case, when using its content, full name of the author and title of the thesis must be clearly indicated. Reproduction or other forms of for profit use or public communication from outside TDX service is not allowed. Presentation of its content in a window or frame external to TDX (framing) is not authorized either. These rights affect both the content of the thesis and its abstracts and indexes.

This paper presents a new Parallel Algorithm for computing a Longest Common Subsequence in Multiple DNA Sequences. It uses a heuristic approach. Although a lot of research has been carried out to find LCS from the two or more given sequences of Protein, DNA, RNA etc, but not many parallel methods exists for finding LCS from multiple sequences. Normally in existing algorithms the time complexity for finding the LCS increases linearly with the increase in Sequences. This is an attempt to given an effective Parallel algorithm to find LCS from any given number of DNA sequences. Significance of this algorithm is that time complexity does not increase linearly with the increase in the number of sequences. However algorithm can also be applied to Protein sequences with the same effectiveness, though the requirement of processors will go up.

Gi are functions from [P(A*)]" into P(A*), i = 1 .... , n, P(A*) denoting the set of all languages over A. Furthermore the G~ are expressible ir~ terms of set-operations, concatenations, and stars which involve the variables X, as well as certain fixed languages° In this note we investigate existence and uniqiuenes~ of solutions of a certain subclass of generalized language equations. Furthermore we show that a soiution is regular if all fixed languages are regular.

We consider systems of equations of the form Xi=,IJ,a l &~LJ& i=l,...,n where A is the underlying alphabet, the Xi are variables, the Pi.0 are boolean functions in the variables J&B and each & is either the empty word or the empty set. The symbolsand u denote concatenation and union of languages over A. We show that any such system has a unique solution which, moreover, is regular. These equations correspond to a type of automaton, called boolean automaton, which is a generalization of a nondeterministic automaton. The equations are then used to determine the language accepted by a sequential network; they are obtainable directly from the network.

Many varieties of regular languages have characterizations in terms of forbidden-patterns of their accepting finite automata. The use of patterns while inferring languages belonging to those families through the RP N I-Lang algorithm help to avoid overgeneralization in the same way as negative samples do. The aim of this paper is to describe and prove the convergence of a modification of the RP N I-Lang algorithm that we call F CRP NI. Preliminary experiments done seem to show that the convergence when we use F CRP NI for some subfamilies of regular languages is achieved faster than when we use just the RP N I algorithm.

A new general method for inference of regular languages using nondeterministic automata as output has recently been developed and proved to converge. The aim of this paper is to describe and analyze the behavior of two implementations of that method and to compare it with two well known algorithms for the same task. A complete set of experiments has been carried out and the results of the new algorithms improve the existing ones both in recognition rates as in sizes of the output automata.

The aim of the paper is to develop a new algorithm that, with a complete sample as input, identifies the family of regular languages by means of nondeterministic finite automata. It is a states-merging algorithm and one of its main features is that the convergence (which is proved) is achieved independently from the order in which states are merged, that is, merging of states may be done "randomly".

This paper focuses on the problem of discovering a Petri Net model from long event sequences generated by a discrete event system. Precisely, it is assumed that the relations between input and output events (i.e. the observable behaviour of the system) are already modelled by a set of Interpreted Petri Net fragments while the behaviour of the internal state evolutions (i.e. the unobservable behaviour) must be discovered. An approach inspired to net synthesis is proposed. It relies on an optimization-based procedure for the identification of the unobservable net structure and marking.

This paper describes new and efficient algorithms for learning deterministic finite automata. Our approach is primarily distinguished by two features: (1) the adoption of an average-case setting to model the ``typical'' labeling of a finite automaton, while retaining a worst-case model for the underlying graph of the automaton, along with (2) a learning model in which the learner is not provided with the means to experiment with the machine, but rather must learn solely by observing the automaton's output behavior on a random input sequence. The main contribution of this paper is in presenting the first efficient algorithms for learning nontrivial classes of automata in an entirely passive learning model. We adopt an on-line learning model in which the learner is asked to predict the output of the next state, given the next symbol of the random input sequence; the goal of the learner is to make as few prediction mistakes as possible. Assuming the learner has a means of resetting the target machine to a fixed start state, we first present an efficient algorithm that article no. IC972648 23

Beginning with a seminal paper of Rényi, expansions in noninteger real bases have been widely studied in the last forty years. They turned out to be relevant in various domains of mathematics, such as the theory of finite automata, number theory, fractals or dynamical systems. Several results were extended by Daróczy and Kátai for expansions in complex bases. We introduce an adaptation of the so-called greedy algorithm to the complex case, and we generalize one of their main theorems.

Throughput and programmability have always been the central, but generally conflicting concerns for modern IP router designs. Current high performance routers depend on proprietary hardware solutions, which make it difficult to adapt to ever-changing network protocols. On the other hand, software routers offer the best flexibility and programmability, but could only achieve a throughput one order of magnitude lower. Modern GPUs are offering significant computing power, and its dataparallel computing model well matches the typical patterns of packet processing on routers. Accordingly, in this research we investigate the potential of CUDA-enabled GPUs for IP routing applications. As a first step toward exploring the architecture of a GPU based software router, we developed GPU solutions for a series of core IP routing applications such as IP routing table lookup and pattern match. For the deep packet inspection application, we implemented both a Bloom-filter based string matching algorithm and a finite automata based regular expression matching algorithm. A GPU based routing table lookup solution is also proposed in this work. Experimental results proved that GPU could accelerate the routing processing by one order of magnitude. Our work suggests that, with proper architectural modifications, GPU based software routers could deliver significant higher throughput than previous CPU based solutions.

Sampled string matching is an efficient approach to the string matching problem introduced in order to overcome the prohibitive space requirements of indexed matching, on the one hand, and drastically reduce searching time for the online solutions, on the other hand. Known solutions to sampled string matching are able to speed up the searching up to 9 times while using less than 11% of the text size. However, they appear to work efficiently only in the case of natural language texts or, in general, when searching on input sequences over large alphabets. In this paper we extend sampled-string matching to the case of small alphabets obtaining a new efficient solution which turns out to be feasible also for searching biological data like genome or protein sequences. Our solution extends a recent approach called Character Distance Sampling by using condensed characters in order to enlarge the size of the alphabet and speed up the searching process. From our experimental results it turns out that our solution significantly reduces the searching time when compared against previous sampled string matching algorithms. In particular on biological data it leads to reduce the space consumption up to 80% and to speed up the searching up to 96%, thus improving the standard online string matching algorithm up to 99.6% using less than 1% of the original text size.

We are given a line of n identical processors (finite automata) that work synchronously. Each processor can transmit just one bit of information to the neighbour processors (if any) on the left and on the right. The computation starts at time 1 with the leftmost processor in a starting state and all other processors in a quiescent state. Given the time f(n), the problem is to set (synchronize) all the processors in a particular state for the first time, at the very same instant f(n). This problem is also known as the Firing Squad Synchronization Problem and was introduced by Moore in 1964. Mazoyer has given a minimal time solution with the least number of different states (six) and very recently he has given a minimal time solution for the constrained problem in which adjacent processors can exchange only one bit. In this paper we present solutions that synchronize the line at a given time expressed as a function of n. In particular we give solutions that synchronize at the times n log n, nv/~, n 2 and 2 '~. Moreover we also show how to compose solutions in such a way to obtain synchronizing solutions for all times expressed by polynomials with normegative coefficients. Clearly all such solutions work also in the general case when the 1-bit constraint is relaxed. 1 * Work partially supported by progetto M.U.R.S.T. grant 60%"Modelli di Sisterni Concorrent," .

A network of identical processors that work synchronously at discrete steps is given. At each step every processor sends messages only to a given subset of its neighboring processors and receives only from the remaining neighbors. The computation starts with one distinguished processor in a particular starting state and all other processors in a quiescent state. The problem is the following: to set all the processors in a given state for the first time and at the very same instant. This problem is known as the firing squad synchronization problem and was introduced in [9]. In this paper solutions are presented that synchronize processors communicating on one-way links arranged in a ring or in a square with rows and columns that are rings. In particular, we provide optimal algorithms to synchronize both of the networks. In addition, compositions of solutions are shown and solutions which synchronize at a time f (n) are given for f (n) equal to n 2 , n log n, and 2 n .

The present dissertation investigates the relationships between classical and nonclassical logics within a common logical platform, in which it is possible to address philosophical questions. More specifically, the focus of the dissertation lies in applications of relevant logics to problems in formal epistemology, such as the problem of logical omnisicence, the distinction between explicit and implicit beliefs, and the modeling of belief revision. As the main contribution of the present work, I devise so-called contextual modal logics, i.e. modal logics where modal operators individuate the range of application of a given logic, to be chosen from the class of extensions of weak relevant logics. In this way, I argue that it is possible to adequately formalise the context-sensitivity of reasoning, a feature which arises when we confront reasoning about the factual and the epistemic domain. Contextual modal logics are presented both semantically and proof-theoretically, by means of Hilbert-style axiom systems. The language of the logics is modularly extended, from the basic relevant language, so as to include topic sensitive operators, implicit belief operators and dynamic operators. Characterisation results are obtained for all extensions of the logics in the contextual modal family.

Abstract. We compare tools for complementing nondeterministic Büchi automata with a recent termination-analysis algorithm. Complementation of Büchi automata is a key step in program verification. Early constructions using a Ramsey-based argument have been supplanted by rank-based constructions with exponentially better bounds. In 2001 Lee et al. presented the size-change termination (SCT) problem, along with both a reduction to Büchi automata and a Ramsey-based algorithm. The Ramsey-based algorithm was presented as a more practical alternative to the automata-theoretic approach, but strongly resembles the initial complementation constructions for Büchi automata. We prove that the SCT algorithm is a specialized realization of the Ramsey-based complementation construction. To do so, we extend the Ramsey-based complementation construction to provide a containment-testing algorithm. Surprisingly, empirical analysis suggests that despite the massive gap in worst-case complexity, Rams...

In this study, we introduce the concept of lattice-valued regular expressions. Such expressions become not only the necessary tool for the analysis and synthesis of fuzzy automata, but give rise to a recursive generation of the family of fuzzy languages accepted by fuzzy automata from certain simple fuzzy languages. We show that the family of fuzzy languages accepted by deterministic

This thesis introduces and describes a software tool called Mushroom which automates the analysis of network protocols specified by the Systems of Communicating Machines (SCM) and the Communicating Finite State Machines (CFSM) models. SCM is a formal model for the specification, verification, and testing of communication protocols. This model was originally developed to improve the CFSM model which is a simpler and earlier Formal Description Technique (FDT). The program is developed as two separate programs in the Ada programming language. The first program automates either the system state analysis (Smart Mushroom), or the full global analysis (Big Mushroom) for a protocol specified by the SCM model. The second program called Simple Mushroom, automates the global reachability analysis for the CFSM model. Mushroom greatly facilitates the use of these models for protocol design and analysis. The run time and memory efficiency of a previous program was improved to allow the analysis of larger and more complex protocols. The program was also extended to accept up to eight machines (processes) in the protocol specification. The user interface of the program has also been improved. Mushroom has been used to verify some well known protocols specified by the SCM and CFSM models such as the token bus protocol, Go Back N and Lap-B data link control protocol.

We present a general framework for the formal speci cation and algorithmic analysis of hybrid systems. A h ybrid system consists of a discrete program with an analog environment. We m o d e l h ybrid systems as nite automata equipped with variables that evolve c o n tinuously with time according to dynamical laws. For veri cation purposes, we restrict ourselves to linear hybrid systems, where all variables follow piecewise-linear trajectories. We p r o vide decidability and undecidability results for classes of linear hybrid systems, and we s h o w that standard program-analysis techniques can be adapted to linear hybrid systems. In particular, we consider symbolic model-checking and minimization procedures that are based on the reachability analysis of an in nite state space. The procedures iteratively compute state sets that are de nable as unions of convex polyhedra in multidimensional real space. We also present approximation techniques for dealing with systems for which the iterative procedures do not converge.

We present a general framework for the formal speci cation and algorithmic analysis of hybrid systems. A h ybrid system consists of a discrete program with an analog environment. We m o d e l h ybrid systems as nite automata equipped with variables that evolve c o n tinuously with time according to dynamical laws. For veri cation purposes, we restrict ourselves to linear hybrid systems, where all variables follow piecewise-linear trajectories. We p r o vide decidability and undecidability results for classes of linear hybrid systems, and we s h o w that standard program-analysis techniques can be adapted to linear hybrid systems. In particular, we consider symbolic model-checking and minimization procedures that are based on the reachability analysis of an in nite state space. The procedures iteratively compute state sets that are de nable as unions of convex polyhedra in multidimensional real space. We also present approximation techniques for dealing with systems for which the iterative procedures do not converge.

The venue for the conference was the Parkhotel Schönbrunn in immediate vicinity of Schönbrunn Palace, which, together with its ancillary buildings and extensive park, is by virtue of its long and colourful history one of the most important cultural monuments in Austria. Vienna, located in the heart of central Europe, is an old city whose historical role as the capital of a great empire and the residence of the Habsburgs is reflected in its architectural monuments, its famous art collections and its rich cultural life, in which music has always played an important part. The workshop was partially supported by the Institute of Computer Languages of the Vienna University of Technology, the Centre for Discrete Mathematics and Theoretical Computer Science of the University of Auckland, the Kurt Gödel Society, and the OCG (Austrian Computer Society); we extend to all our gratitude.

Population protocols have been introduced as a model of sensor networks consisting of very limited mobile agents with no control over their own movement. A population protocol corresponds to a collection of anonymous agents, modeled by finite automata, that interact with one another to carry out computations, by updating their states, using some rules. Their computational power has been investigated under several hypotheses but always when restricted to finite size populations. In particular, predicates stably computable in the original model have been characterized as those definable in Presburger arithmetic. In this paper, we study mathematically a particular population protocol that we show to compute in some natural sense some algebraic irrational number, whenever the population goes to infinity. Hence we show that these protocols seem to have a rather different computational power when considered as computing functions, and when a huge population hypothesis is considered. The computational power of networks of finitely many anonymous resourcelimited mobile agents has been investigated in several recent papers. In partic-

The framework of Finite-State Intersection Grammars employs a parsing technique according to which several finite-state automata are intersected to determine the output automaton. Implementation of the intersection parser has turned out to be a difficult task. Several problems in efficiency arise when disambiguation choices are based on long contexts with many don't cares. We are concerned with the long-distance effects of the grammatical constraints. We outline a compacting method that rearranges the search space of the intersection process and makes it shallower. This method is based on the specialization of grammar rules relative to each input sentence.