Introducing Vaucanson

2012

This book constitutes the thoroughly refereed papers of the 17th International Conference on Implementation and Application of Automata, CIAA 2012, held in Porto, Portugal, in July 2012. The 21 revised full papers presented together with 5 invited papers and 7 short papers were carefully selected from 53 submissions. The papers cover various topics such as automata applications in formal verification methods, natural language processing, pattern matching, data storage and retrieval, and bioinformatics, as well as theoretical ...

Language and Automata Theory and Applications, 2017

We investigate the computational power of affine automata (AfAs) introduced in [4]. In particular, we present a simpler proof for how to change the cutpoint for any affine language and a method how to reduce error in bounded error case. Moreover, we address to the question of [4] by showing that any affine language can be recognized by an AfA with certain limitation on the entries of affine states and transition matrices. Lastly, we present the first languages shown to be not recognized by AfAs with bounded-error.

Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '90, 1990

We compare and contrast several techniques for the implementation o f c o m p o n e n ts of an algebraic manipulation system. On one hand is the mathematicalalgebraic approach which c haracterizes (for example) IBM's Scratchpad II. On the other hand is the more ad hoc approach which c haracterizes many other popular systems (for example, Macsyma, Reduce, Maple, and Mathematica). While the algebraic approach h a s generally positive results, careful examination suggests that there are signi cant remaining problems, especially in the representation and manipulation of analytical, as opposed to algebraic mathematics. We describe some of these problems, and some general approaches for solutions.

2008

Finite state automata are Turing machines with fixed finite bounds on resource use. Automata lend themselves well to real-time computations and efficient algorithms. Continuing a tradition of studying computability in mathematics, we examine automatic structures, mathematical objects which can be represented by automata, and apply resulting observations to computer science. We measure the complexity of automatic structures via well-established concepts from model theory, topology, and set theory. We prove the following results. The ordinal height of any automatic well-founded partial order is bounded by ω ω. The ordinal heights of automatic well-founded relations are unbounded below ω CK 1 , the first uncomputable ordinal. For any computable ordinal α, there is an automatic structure of Scott rank at least α. Moreover, there are automatic structures of Scott rank ω CK 1 , ω CK 1 + 1. For any computable ordinal α, there is an automatic successor tree of Cantor-Bendixson rank α. Next, we study infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations have finite degree and can be described by finite automata over a one-letter alphabet. We investigate algorithmic properties of such graphs in terms of their finite presentations. In particular, we ask how hard it is to check whether a given node belongs to an infinite component, whether two given nodes in the graph are reachable from one another, and whether the graph is connected. We give polynomial-time algorithms answering each of these questions. For a fixed input graph, the algorithm for infinite component membership works in constant time and reachability is decided uniformly by a single automaton. Hence, we improve on previous work, in which nonelementary or nonuniform algorithms were found. We turn our attention to automata techniques for deciding first-order logical theories. These techniques are useful in Integer Linear Programming and Mixed Integer Linear Programming, which in turn have applications in diverse areas of computer science and engineering. We extend known work to address the enumeration problem for linear programming solutions. Then, we apply a similar paradigm to give an automata theoretic decision procedure for the p-adic valued ring under addition and for formal Laurent series over a finite field with valuation and addition. BIOGRAPHICAL SKETCH Mor Minnes was born in Haifa, Israel in 1982. From an early age, Mor learned the importance of words and education: in the bath, Mor's parents (both students at the time) saw her and her sister typing intently on imaginary typewriters and proclaiming that they were working. In 1989, the nuclear family (now also including two brothers) moved to Vancouver, Canada for what was intended as a short visit for Mor's father to do a residency in psychiatry. Quickly, Mor became Mia, choosing a more suitable English name at the suggestion of her maternal grandmother. The family settled in Vancouver and Mia attended Prince of Wales Mini School and the International Baccalaureate Program at Sir Winston Churchill Secondary School. While in high school, Mia enjoyed both the sciences and the humanities. Not willing to give up either of these, Mia decided to pursue dual Bachelor's degrees at Queen's University in Kingston, Ontario. In 1999, Mia headed to snowy Kingston and enrolled in Applied Science (Mathematics & Engineering, Computing and Communications) and Philosophy. Mia had her first encounter with programming and fell in love with the power behind logical thinking. Considering graduate studies, logic was a natural fit with Mia's interests as it lay in the intersection of her favourite philosophy courses (philosophy of language and science) and engineering courses (computer architecture, programming, and math). Her best friend compiled a list of graduate programs in logic and Mia started browsing through their websites. When she discovered Anil Nerode's research outlining connections between automata, logic, and hybrid systems, she knew she had found what she wanted to work on. Mia graduated from Queen's and headed south to Ithaca, NY to begin graduate school in mathematics at Cornell University, along the way also earning a Master's degree in computer science. After five years of graduate school, Mia is looking forward to being a C.L.E. Moore Instructor at MIT next year.

2007

Abstract We review, in a unified framework, translations from five different logics—monadic second-order logic of one and two successors (S1S and S2S), linear-time temporal logic (LTL), computation tree logic (CTL), and modal µ-calculus (MC)—into appropriate models of finite-state automata on infinite words or infinite trees. Together with emptiness-testing algorithms for these models of automata, this yields decision procedures for these logics.

Natural Computing, 2021

We present new results on the computational limitations of affine automata (AfAs). First, we show that using the endmarker does not increase the computational power of AfAs. Second, we show that the computation of bounded-error rational-valued AfAs can be simulated in logarithmic space. Third, we identify some logspace unary languages that are not recognized by algebraic-valued AfAs. Fourth, we show that using arbitrary real-valued transition matrices and state vectors does not increase the computational power of AfAs in the unbounded-error model. When focusing only the rational values, we obtain the same result also for bounded error. As a consequence, we show that the class of bounded-error affine languages remains the same when the AfAs are restricted to use rational numbers only.

2003

We present a system that performs computations on finite state machines, syntactic semigroups, and one-dimensional cellular automata.

2000

Lecture Notes in Computer Science, 2008

This paper discusses the pros and cons of using a functional language for implementing a computer algebra system. The contributions of the paper are twofold. Firstly, we discuss some language-centered design aspects of a computer algebra system -the "language unity" concept. Secondly, we provide an implementation of a fast polynomial multiplication algorithm, which is one of the core elements of a computer algebra system. The goal of the paper is to test the feasibility of an implementation of (some elements of) a computer algebra system in a modern functional language.

Lecture Notes in Computer Science, 2000

This paper presents an overview of algorithms for constructing automata from linear arithmetic constraints. It identifies one case in which the special structure of the automata that are constructed allows a linear-time determinization procedure to be used. Furthermore, it shows through theoretical analysis and experiments that the special structure of the constructed automata does, in quite a general way, render the usual upper bounds on automata operations vastly overpessimistic. This research was partially funded by a grant of the "Communauté française de Belgique -Direction de la recherche scientifique -Actions de recherche concertées".