Topic
Formal language
About: Formal language is a research topic. Over the lifetime, 5763 publications have been published within this topic receiving 154114 citations.
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12 Aug 2006
TL;DR: It is shown that satisfiability for the two-variable first-order logic FO2(~,<,+1) is decidable over finite and over infinite data words, where ~ is a binary predicate testing the data value equality and +1,< are the usual successor and order predicates.
Abstract: In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the two-variable first-order logic FO^2(~,\le,+1) is decidable over finite and over infinite data words, where i« is a binary predicate testing the data value equality and +1,\le are the usual successor and order predicates. The complexity of the problem is at least as hard as Petri net reachability. Several extensions of the logic are considered, some remain decidable while some are undecidable.
220 citations
01 Jan 2002
TL;DR: A translation of stochastic lambda calculus into measure terms is given, which can not only denote discrete probability distributions but can also support the best known modeling techniques.
Abstract: Probability distributions are useful for expressing the meanings of probabilistic languages, which support formal modeling of and reasoning about uncertainty. Probability distributions form a monad, and the monadic definition leads to a simple, natural semantics for a stochastic lambda calculus, as well as simple, clean implementations of common queries. But the monadic implementation of the expectation query can be much less efficient than current best practices in probabilistic modeling. We therefore present a language of measure terms, which can not only denote discrete probability distributions but can also support the best known modeling techniques. We give a translation of stochastic lambda calculus into measure terms. Whether one translates into the probability monad or into measure terms, the results of the translations denote the same probability distribution.
219 citations
TL;DR: The proposed methods are illustrated through syntactic pattern recognition experiments in which a number of strings generated by ten given (source) non-k- TSSL grammars are used to infer ten k-TSSL stochastic automata, which are further used to classify newstrings generated by the same source Grammars.
Abstract: The inductive inference of the class of k-testable languages in the strict sense (k-TSSL) is considered. A k-TSSL is essentially defined by a finite set of substrings of length k that are permitted to appear in the strings of the language. Given a positive sample R of strings of an unknown language, a deterministic finite-state automation that recognizes the smallest k-TSSL containing R is obtained. The inferred automation is shown to have a number of transitions bounded by O(m) where m is the number of substrings defining this k-TSSL, and the inference algorithm works in O(kn log m) where n is the sum of the lengths of all the strings in R. The proposed methods are illustrated through syntactic pattern recognition experiments in which a number of strings generated by ten given (source) non-k-TSSL grammars are used to infer ten k-TSSL stochastic automata, which are further used to classify new strings generated by the same source grammars. The results of these experiments are consistent with the theory and show the ability of (stochastic) k-TSSLs to approach other classes of regular languages. >
218 citations
Book•
08 Sep 2008TL;DR: Many topics often absent from other textbooks, such as repetitions in words, state complexity, the interchange lemma, 2DPDAs, and the incompressibility method are covered here.
Abstract: Intended for graduate students and advanced undergraduates in computer science, A Second Course in Formal Languages and Automata Theory treats topics in the theory of computation not usually covered in a first course. After a review of basic concepts, the book covers combinatorics on words, regular languages, context-free languages, parsing and recognition, Turing machines, and other language classes. Many topics often absent from other textbooks, such as repetitions in words, state complexity, the interchange lemma, 2DPDAs, and the incompressibility method, are covered here. The author places particular emphasis on the resources needed to represent certain languages. The book also includes a diverse collection of more than 200 exercises, suggestions for term projects, and research problems that remain open.
218 citations
18 Oct 1967
TL;DR: The notion of an abstract family of languages (AFL) as a family of sets of words satisfying certain properties common to many types of formal languages is introduced and operations preserving AFL are considered.
Abstract: The notion of an abstract family of languages (AFL) as a family of sets of words satisfying certain properties common to many types of formal languages is introduced. Operations preserving AFL are then considered. The concept of an abstract family of acceptors (AFA) is also introduced and shown to give rise to an AFL. A necessary and sufficient condition on an AFL is presented in order that the AFL come from some AFA. Finally, abstract families of transducers (AFA with output) are discussed.
216 citations