weighted automata

Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system depends on the decisions of both players, supplemented by chance. In this work, we focus on the notion of randomised strategy. More specifically, we show that three natural definitions may lead to very different results: in the most general cases, an almost-surely winning situation may become almost-surely losing if the player is only allowed to use a weaker notion of strategy. In more reasonable settings, translations exist, but they require infinite memory, even in simple cases. Finally, some traditional problems becomes undecidable for the strongest type of strategies. “You can’t have a strategy against telepaths: you have to act randomly. You have to not know what you’re going to do next. You have to shut your eyes and run blindly. The problem is: h...

We study determinization of weighted finite-state automata (WFAs), which has important applications in automatic speech recognition (ASR). We provide the first polynomial-time algorithm to test for the twins property, which determines if a WFA admits a deterministic equivalent. We also provide a rigorous analysis of a determinization algorithm of Mohri, with tight bounds for acyclic WFAs. Given that WFAs can expand exponentially when determinized, we explore why those used in ASR tend to shrink. The folklore explanation is that ASR WFAs have an acyclic, multi-partite structure. We show, however, that there exist such WFAs that always incur exponential expansion when determinized. We then introduce a class of WFAs, also with this structure, whose expansion depends on the weights: some weightings cause them to shrink, while others, including random weightings, cause them to expand exponentially. We provide experimental evidence that ASR WFAs exhibit this weight dependence. That they shrink when determinized, therefore, is a result of favorable weightings in addition to special topology.

Cost register automata (CRAs) are one-way finite automata whose transitions have the side effect that a register is set to the result of applying a state-dependent semiring operation to a pair of registers. Here it is shown that CRAs over the tropical semiring (N ∪ {∞}, min, +) can simulate polynomial time computation, proving along the way that a naturally defined width-k circuit value problem over the tropical semiring is Pcomplete. Then the copyless variant of the CRA, requiring that semiring operations be applied to distinct registers, is shown no more powerful than NC 1 when the semiring is (Z, +, ×) or (Γ * ∪{⊥}, max, concat). This relates questions left open in recent work on the complexity of CRA-computable functions to long-standing class separation conjectures in complexity theory, such as NC versus P and NC 1 versus GapNC 1 .

We study determinization of weighted finite-state automata (WFAs), which has important applications in automatic speech recognition (ASR). We provide the first polynomial-time algorithm to test for the twins property, which determines if a WFA admits a deterministic equivalent. We also provide a rigorous analysis of a determinization algorithm of Mohri, with tight bounds for acyclic WFAs. Given that WFAs can expand exponentially when determinized, we explore why those used in ASR tend to shrink. The folklore explanation is that ASR WFAs have an acyclic, multi-partite structure. We show, however, that there exist such WFAs that always incur exponential expansion when determinized. We then introduce a class of WFAs, also with this structure, whose expansion depends on the weights: some weightings cause them to shrink, while others, including random weightings, cause them to expand exponentially. We provide experimental evidence that ASR WFAs exhibit this weight dependence. That they shrink when determinized, therefore, is a result of favorable weightings in addition to special topology.

We discuss uncertainty propagation in reaction history data from underground nuclear tests. γ reaction history detectors measured flux as a function of time. After data analysis we report α as a function of time. Flux uncertainty and time uncertainty propagation into α uncertainty are discussed in detail. Discretization of the formulas is discussed.

The notion of switchable languages has been defined by Kumar, Takai, Fabian and Ushio in [11]. It deals with switching supervisory control, where switching means switching between two specifications. In this paper, we first extend the notion of switchable languages to n languages, (n ≥ 3). Then we consider a discrete-event system modeled with weighted automata. The use of weighted automata is justified by the fact that it allows us to synthesize a switching supervisory controller based on the cost associated to each event, like the energy for example. Finally the proposed methodology is applied to a simple example.

En este artículo, nosotros proponemos un enfoque para generar una planificación fundamentada en los conceptos de k-interacción y consenso, mostrando para ello un algoritmo que acopla la planta con dichos conceptos. En este sentido, se reducirán los modelos resultantes y en consecuencia la complejidad computacional.

We introduce the notion of strongly distributed fuzzy systems and present a uniform approach to incremental problem solving on them. The approach is based on the systematic use of two logical reduction techniques: Feferman-Vaught reductions and syntactically defined translation schemes. The fuzzy systems are presented as logical structures A's. The problems are presented as fuzzy formulae on them. We propose a uniform template for methods, which allow (for a certain cost) evaluation of formulae of fuzzy logic L over A from values of formulae over its components and values of formulae over the index structure I.

Weighted automata are a generalization of non-deterministic automata where each transition, in addition to an input letter, has also a quantity expressing the weight (e.g. cost or probability) of its execution. As for non-deterministic automata, their behaviours can be expressed in terms of either (weighted) bisimilarity or (weighted) language equivalence. Coalgebras provide a categorical framework for the uniform study of state-based systems and their behaviours. In this work, we show that coalgebras can suitably model weighted automata in two different ways: coalgebras on Set (the category of sets and functions) characterize weighted bisimilarity, while coalgebras on V ect (the category of vector spaces and linear maps) characterize weighted language equivalence. Relying on the second characterization, we show three different procedures for computing weighted language equivalence. The first one consists in a generalizion of the usual partition refinement algorithm for ordinary automata. The second one is the backward version of the first one. The third procedure relies on a syntactic representation of rational weighted languages.

Decidability of the determinization problem for weighted automata over the semiring (Z∪{−∞}, max, +), WA for short, is a long-standing open question. We propose two ways of approaching it by constraining the search space of deterministic WA: k-delay and r-regret. A WA N is k-delay determinizable if there exists a deterministic automaton D that defines the same function as N and for all words α in the language of N , the accepting run of D on α is always at most k-away from a maximal accepting run of N on α. That is, along all prefixes of the same length, the absolute difference between the running sums of weights of the two runs is at most k. A WA N is r-regret determinizable if for all words α in its language, its non-determinism can be resolved on the fly to construct a run of N such that the absolute difference between its value and the value assigned to α by N is at most r. We show that a WA is determinizable if and only if it is k-delay determinizable for some k. Hence deciding the existence of some k is as difficult as the general determinization problem. When k and r are given as input, the k-delay and r-regret determinization problems are shown to be EXPtimecomplete. We also show that determining whether a WA is r-regret determinizable for some r is in EXPtime.

Weighted automata model quantitative features of the behavior of systems and have been investigated for various structures like words, trees, traces, pictures, and nested words. In this paper, we introduce a general model of weighted automata acting on graphs, which form a quantitative version of Thomas' unweighted model of graph acceptors. We derive a Nivat theorem for weighted graph automata which shows that their behaviors are precisely those obtainable from very particular weighted graph automata and unweighted graph acceptors with a few simple operations. We also show that a suitable weighted MSO logic is expressively equivalent to weighted graph automata. As a consequence, we obtain corresponding Büchi-type equivalence results known from the recent literature for weighted automata and weighted logics on words, trees, pictures, and nested words. Establishing such a general result has been an open problem for weighted logic for some time.

In this paper the Van Der Laan hybrid sequence is introduced. Binet-like-formula, partial sum and generating function related to this sequence are obtained. Some interesting properties of Van Der Laan hybrid sequence are given. Finally, the eigenvalues and determinant of a circulant matrix involving Van Der Laan hybrid sequence are represented.

We present an XML format that allows to describe a large class of finite weighted automata and transducers. Our design choices stem from our policy of making the implementation as simple as possible. This format has been tested for the communication between the modules of our automata manipulation platform Vaucanson, but this document is less an experiment report than a

A small device with WiFi multi-sensing element is very important under a social digital century. This study aims to implement the hardware and the power of the algorithm with WiFi technologies. Especially, the multi-sensors have to reinforce around a home area and support to any requirement in the term of digital society. This study focus to care the home security— on going to the fire detection with applying several technologies based on a Cloud. Firstly, the multi-sensor calibration has used calibration time and self-calibration as the Finite Impulse Response (FIR). Next, the Full-Scale Kalman Filter (FSKF) helps to fill data and estimate the accuracy data. After that, the fire detection mechanism has used Fuzzy logic to detect and send alert messages over an IFTTT process. There are changed following event-- the data range of fire proportion inside the home. Furthermore, The OFF-Mode has reduced the power consumption suddenly the WiFi module is sent the sensor data to the Cloud. ...

In this article, we will propose an approach to generate a planning based on the concepts of k-interaction and consensus, showing for this an algorithm that couples the plant with these concepts. In this sense, the resulting models will be reduced and, consequently the computational complexity.

En este artículo, nosotros proponemos un enfoque para generar una planificación fundamentada en los conceptos de k-interacción y consenso, mostrando para ello un algoritmo que acopla la planta con dichos conceptos. En este sentido, se reducirán los modelos resultantes y en consecuencia la complejidad computacional.

One of ways to facilitate process of information retrieval is by performing clustering toward collection of the existing documents. The existing text documents are often unstructured. The forms are varied and their groupings are ambiguous. This cases cause difficulty on information retrieval process. Moreover, every second new documents emerge and need to be clustered. Generally, static document clustering method performs clustering of document after whole documents are collected. However, performing re-clustering toward whole documents when new document arrives causes inefficient clustering process. In this paper, we proposed a new method for document clustering with dynamic hierarchy algorithm based on fuzzy set type - II from frequent itemset. To achieve the goals, there are three main phases, namely: determination of key-term, the extraction of candidates clusters and cluster hierarchical construction. Based on the experiment, it resulted the value of F-measure 0.40 for Newsgrou...

Let GG = (VV,EE) is a graph and kk is a positive integers. Total labeling-kk on GG is a mapping ff:VV ∪ EE ⟶ {1,2, ... ,kk}. The weight of the vertex xx is represented by wwff(xx) = ff(xx) + ∑ λλ(uuxx) uuuu∈EE and the weight of the edge xxxx is represented by wwλλ(xxxx) = λλ(xx) + λλ(xxxx) + ff(xx). A total-kk labeling of GG is called a tottaly irregular total labeling, if the weight of every two distinct vertices are different and the weight of every two distinct edges are different. The minimum kk such that a graph GG has a totally irregular total kklabeling is called the total irregularity strength of GG, denoted by tttt(GG). In this paper obtained tttt(4SSnn) = 2nn + 1 where nn is a positive integer and nn ≥ 3.

In this article, we will propose an approach to generate a planning based on the concepts of k-interaction and consensus, showing for this an algorithm that couples the plant with these concepts. In this sense, the resulting models will be reduced and, consequently the computational complexity.

Considering time and resource limitations in different industries, increases importance and complexity of task scheduling problems where all tasks should be executed in the minimum time. Moreover, integrating uncontrollable tasks in the procedure makes more complexity in this problems. The main objective of our work is to propose a formal model and a tool for automatic scheduling of a system with a specific kind of resource conflict in order to minimize system's makespan as much as possible.

The objective of scheduling problems is to find the optimal performing sequence for a set of tasks by respecting predefined constraints and optimizing a cost: time, energy, etc. Despite classical approaches, automata models are expressive and also robust against changes in the parameter setting and against changes in the problem specification. Besides, few studies have used formal verification approaches for addressing scheduling problems; yet none of them considered challenging and practical issues such as multi-resource sharing aspect, uncontrollable environment and reaching the optimal schedule in a reasonable time for industrializing the model. The main objective of this thesis is to propose an efficient modeling and solving approach for the scheduling problem, considering multi-resource sharing and potential uncertainty in occurrence of certain events. For this purpose, after an introduction in Chapter 1, Chapter 2 addresses the problem of scheduling through a visual, expressiv...

The notion of switchable languages has been defined by Kumar, Takai, Fabian and Ushio in [11]. It deals with switching supervisory control, where switching means switching between two specifications. In this paper, we first extend the notion of switchable languages to n languages, (n ≥ 3). Then we consider a discrete-event system modeled with weighted automata. The use of weighted automata is justified by the fact that it allows us to synthesize a switching supervisory controller based on the cost associated to each event, like the energy for example. Finally the proposed methodology is applied to a simple example.

A supervisor is said to be mutually nonblocking with respect to a pair of speci-cations if upon completing a task in any of the specications, it can continue on to complete the task in the other specication, i.e., the two specications do not block each other. The notion of mutually nonblocking supervisor was introduced in [4, 5]. In this paper we present an algorithm of polynomial complexity for computing a maximally permissive mutually and globally nonblocking supervisor. In case such a supervisor does not exist, we present a technique for relaxing the specications for which a super-visor exists. The algorithms are based on a notion of attractability, and as a special case oer a new way of computing the maximally permissive nonblocking supervisors. The results are then applied to design of maximally permissive switching supervisors so as to allow for switching between the specications at any time while the system is executing.

In this paper, it is proven that the diameter of the graph of a semiring with more than two elements does not exceed three. Introduction. Y. F. Lin and J. S. Ratti [1], [2], [3] studied the graphs of semirings and conjectured that: (a) The graph of a semiring that contains more than two elements is connected. (b) The diameter of the above-mentioned graph does not exceed three. Starting from the results they obtained, we are going to prove that both of these conjectures are correct. To clarify the terms of this paper, we will first review some basic definitions: A semiring is a nonempty set equipped with two operations: addition, +, and multiplication (denoted by juxtaposition), such that addition is associative and commutative and multiplication associative and distributive across addition both from the left and the right.

We present pumping lemmas for five classes of functions definable by fragments of weighted automata over the min-plus semiring, the max-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of functions definable by unambiguous, finitely-ambiguous, polynomially-ambiguous weighted automata, and the full class of weighted automata is strict for the min-plus and max-plus semirings.

We present pumping lemmas for five classes of functions definable by fragments of weighted automata over the min-plus semiring, the max-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of functions definable by unambiguous, finitely-ambiguous, polynomially-ambiguous weighted automata, and the full class of weighted automata is strict for the min-plus and max-plus semirings.

The notion of switched discrete event systems (DES) has been introduced recently. This is a class of DES where each automaton is the composition of two basic automata, but with different composition operators. A switching occurs when there is a change of the composition operator, but keeping the same two basic automata. A mode behavior is defined as the active DES behavior for a given composition operator. Composition operators are supposed to change more than once so that each mode is visited more than once. In this paper we study the modeling and control of an experimental manufacturing system as an example of switched DES.

The Parikh matrix mapping was introduced by Mateescu et al. in 2001 as a canonical generalization of the classical Parikh mapping. The injectivity problem of Parikh matrices, even for ternary case, has withstanded numerous attempts over a decade by various researchers, among whom is Serbanuta. Certain M-ambiguous words are crucial in Serbanuta's findings about the number of M-unambiguous prints. We will show that these words are in fact strongly M-ambiguous, thus suggesting a possible extension of Serbanuta’s work to the context of strong M-equivalence. In addition, initial results pertaining to a related conjecture by Serbanuta will be presented.

The notion of switchable languages has been defined by Kumar, Takai, Fabian and Ushio in [11]. It deals with switching supervisory control, where switching means switching between two specifications. In this paper, we first extend the notion of switchable languages to n languages, (n ≥ 3). Then we consider a discrete-event system modeled with weighted automata. The use of weighted automata is justified by the fact that it allows us to synthesize a switching supervisory controller based on the cost associated to each event, like the energy for example. Finally the proposed methodology is applied to a simple example.

We present three pumping lemmas for three classes of functions definable by fragments of weighted automata over the min-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of functions definable by unambiguous, finitely-ambiguous, polynomially-ambiguous weighted automata, and the full class of weighted automata is strict for the min-plus semiring. 2012 ACM Subject Classification Theory of computation → Models of computation

Cost register automata (CRA) and its subclass, copyless CRA, were recently proposed by Alur et al. as a new model for computing functions over strings. We study some structural properties, expressiveness, and closure properties of copyless CRA. We show that copyless CRA are strictly less expressive than weighted automata and are not closed under reverse operation. To find a better class we impose restrictions on copyless CRA, which ends successfully with a new robust computational model that is closed under reverse and other extensions.