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Finite Semigroups and Recognizable Languages An Introduction
, 1995
"... This paper is an attempt to share with a larger audience some modern developments in the theory of finite automata. It is written for the mathematician who has a background in semigroup theory but knows next to nothing on automata and languages. No proofs are given, but the main results are illustra ..."
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Cited by 30 (9 self)
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This paper is an attempt to share with a larger audience some modern developments in the theory of finite automata. It is written for the mathematician who has a background in semigroup theory but knows next to nothing on automata and languages. No proofs are given, but the main results are illustrated by several examples and counterexamples
Learning ktestable and kpiecewise testable languages from positive data
 GRAMMARS
, 2004
"... The families of locally testable (LT) and piecewise testable (PWT) languages have been deeply studied in formal language theory. They have in common that the role played by the segments of length k of their words in the first family is played in the second by their subwords (sequences of non necessa ..."
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Cited by 8 (0 self)
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The families of locally testable (LT) and piecewise testable (PWT) languages have been deeply studied in formal language theory. They have in common that the role played by the segments of length k of their words in the first family is played in the second by their subwords (sequences of non necessarily consecutive symbols), also of length k. We propose algorithms that, given k>0, identify both families of languages (kPWT and kLT) from positive data in the limit. The first one identifies the family of kPWT languages making use of a combinatorial property discovered by Simon and improves the complexity of a previous algorithm for that family [25]. The second algorithm identifies the family of kLT languages using a result about the cascade product of automata. In this product, for each k, one of the factors is a fixed transducer and the second is the automaton obtained by the first algorithm for k = 1 using the transduction of the sample as input.
Generalized Deterministic Languages and their Automata: A Characterization of Restricted Temporal Logic
 INST. FUR INFORMATIK, UNIV. WURZBURG
, 1999
"... Let TL[X; F] (TL[F]) be the class of formulas of temporal logic, where as the only temporal operators X (next) and F (eventually) are allowed (only F is allowed, resp.). For a class \Phi ` TL[X; F] let L(\Phi) be the class of \Phidefinable languages. Among others, characterizations of L(TL[X; F]) ..."
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Cited by 4 (1 self)
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Let TL[X; F] (TL[F]) be the class of formulas of temporal logic, where as the only temporal operators X (next) and F (eventually) are allowed (only F is allowed, resp.). For a class \Phi ` TL[X; F] let L(\Phi) be the class of \Phidefinable languages. Among others, characterizations of L(TL[X; F]) and L(TL[F]) in terms of forbidden patterns in finite automata are known. Here we ask for every bound k 0 on the number of nested uses of the next operator for the expressive power of the respective fragment of TL[X; F]. Denote by TL[X(k); F] the class of formulas in TL[X; F] with nesting depth k in the next operator. Obviously, L(TL[X; F]) = S k0 L(TL[X(k); F]) and L(TL[F]) = L(TL[X(0); F]). We prove a levelwise characterization of the above syntactical hierarchy (1) in terms of a certain pattern S rev k (cf. Figure 6) that must not appear in the transition graph of deterministic finite automata, and (2) in terms of a formal language representation involving kleftdeterministic lan...
Theme and variations
"... Abstract. The concatenation product is one of the most important operations on regular languages. Its study requires sophisticated tools from algebra, finite model theory and profinite topology. This paper surveys research advances on this topic over the last fifty years. The concatenation product p ..."
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Abstract. The concatenation product is one of the most important operations on regular languages. Its study requires sophisticated tools from algebra, finite model theory and profinite topology. This paper surveys research advances on this topic over the last fifty years. The concatenation product plays a key role in two of the most important results of automata theory: Kleene’s theorem on regular languages [23] and Schützenberger’s theorem on starfree languages [60]. This survey article surveys the most important results and tools related to the concatenation product, including connections with algebra, profinite topology and finite model theory. The paper is organised as follows: Section 1 presents some useful algebraic tools for the study of the concatenation product. Section 2 introduces the main definitions on the product and its variants. The classical results are summarized in Section 3. Sections 4 and 5 are devoted to the study of two algebraic tools: Schützenberger products and relational morphisms. Closure properties form the topic of Section 6. Hierarchies and their connection with
Finite semigroups and recognizable languages: an introduction
, 2002
"... This paper is an attempt to share with a larger audience some modern developments in the theory of finite automata. It is written for the mathematician who has a background in semigroup theory but knows next to nothing on automata and languages. No proofs are given, but the main results are illustra ..."
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This paper is an attempt to share with a larger audience some modern developments in the theory of finite automata. It is written for the mathematician who has a background in semigroup theory but knows next to nothing on automata and languages. No proofs are given, but the main results are illustrated by several examples and counterexamples. What is the topic of this theory? It deals with languages, automata and semigroups, although recent developments have shown interesting connections with model theory in logic, symbolic dynamics and topology. Historically, in their attempt to formalize natural languages, linguists such as Chomsky gave a mathematical definition of natural concepts such as words, languages or grammars: given a finite set A, a word on A is simply an element of the free monoid on A, and a language is a set of words. But since scientists are fond of classifications of all sorts, language theory didn’t escape to this mania. Chomsky established a first hierarchy, based on his formal grammars. In this paper, we are interested in the recognizable languages, which form the lower level of the