Topic
ω-automaton
About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.
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01 Mar 2000
TL;DR: It is shown that any automatic structure can be characterised in terms of congruences of nite index of a certain partial, and suggested the development of a ner theory, the theory of structures presented by automata is suggested.
Abstract: In this paper we report on some results about nite automata presentablestructures, an area of research rst proposed in a Khoussainov-Nerode paperin 1995 [1]. The topic of automata presentable structures is new, underdevelopment and is on the edge of interactions between automata theory,(universal) algebra, model theory and complexity theory.One motivation for the development of the theory of FA presentablestructures comes from the theory of computable structures, the area devotedto understanding the e ective content of results in model theory and algebra.We refer the interested reader to the Handbook of Recursive Mathematics[2], the Handbook of Computability Theory [3] and the survey paper [4].In the theory of computable structures one naturally assumes that thereare unbounded resources for performing computations and hence the basicmodel of computation is the one of Turing. Cenzer, Nerode and Remmelsuggest the idea of considering feasible computations (e.g. polynomial timecomputations) and investigate the e ect of such computations on results inalgebra and model theory. Research in this area has grown into the theoryof feasible structures (e.g. polynomial time structures), or more generallyinto feasible mathematics [5] [6] [7].In [1] Khoussainov-Nerode suggest the development of a ner theory,the theory of structures presented by automata. Informally, a structure Aof a nite signature is automatic if its domain and all the atomic relationsare recognised by nite automata. Then any structure Bisomorphic to Ais called nite automaton (FA) presentable.InthiscaseAis a FApresentation of B. In [1] it is shown that any automatic structure canbe characterised in terms of congruences of nite index of a certain partial
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TL;DR: It is proved that constructing a Parikh-equivalent automaton for a given CFG is Fixed Parameter Tractable (FPT) when the degree m and regularity width d are parameters.
Abstract: Parikh's theorem states that every Context Free Language (CFL) has the same Parikh image as that of a regular language. A finite state automaton accepting such a regular language is called a Parikh-equivalent automaton. In the worst case, the number of states in any non-deterministic Parikh-equivalent automaton is exponentially large in the size of the Context Free Grammar (CFG). We associate a regularity width d with a CFG that measures the closeness of the CFL with regular languages. The degree m of a CFG is one less than the maximum number of variable occurrences in the right hand side of any production. Given a CFG with n variables, we construct a Parikh-equivalent non-deterministic automaton whose number of states is upper bounded by a polynomial in $n (d^{2d(m+1)}), the degree of the polynomial being a small fixed constant. Our procedure is constructive and runs in time polynomial in the size of the automaton. In the terminology of parameterized complexity, we prove that constructing a Parikh-equivalent automaton for a given CFG is Fixed Parameter Tractable (FPT) when the degree m and regularity width d are parameters. We also give an example from program verification domain where the degree and regularity are small compared to the size of the grammar.
08 Sep 2014
TL;DR: Weak singular hybrid automata (WSHA) is introduced, a previously unexplored subclass of singular Hybrid automata, and the decidability (and the exact complexity) of various verification questions for this class including reachability (NP-Complete) and LTL model-checking (Pspace-Complete).
Abstract: The framework of Hybrid automata—introduced by Alur, Courcourbetis, Henzinger, and Ho—provides a formal modeling and analysis environment to analyze the interaction between the discrete and the continuous parts of hybrid systems. Hybrid automata can be considered as generalizations of finite state automata augmented with a finite set of real-valued variables whose dynamics in each state is governed by a system of ordinary differential equations. Moreover, the discrete transitions of hybrid automata are guarded by constraints over the values of these real-valued variables, and enable discontinuous jumps in the evolution of these variables. Singular hybrid automata are a subclass of hybrid automata where dynamics is specified by state-dependent constant vectors. Henzinger, Kopke, Puri, and Varaiya showed that for even very restricted subclasses of singular hybrid automata, the fundamental verification questions, like reachability and schedulability, are undecidable. Recently, Alur, Wojtczak, and Trivedi studied an interesting class of hybrid systems, called constant-rate multi-mode systems, where schedulability and reachability analysis can be performed in polynomial time. Inspired by the definition of constant-rate multi-mode systems, in this paper we introduce weak singular hybrid automata (WSHA), a previously unexplored subclass of singular hybrid automata, and show the decidability (and the exact complexity) of various verification questions for this class including reachability (NP-Complete) and LTL model-checking (Pspace-Complete). We further show that extending WSHA with a single unrestricted clock or with unrestricted variable updates lead to undecidability of reachability problem.
01 Jan 2006
TL;DR: This paperalyses the accepting a programming language was proved, the equivalence theorem between finite automata and finite automaton became the basic theory of describing regular expressions, points out the problem existing in lexical rules.
Abstract: Thefirst phaseofacompiler islexical analysis, i.e., Theautomaton theory hasbeenwidely applied in designing finite automaton torecognize thetokens ofa manyareasofscience, suchassystem simulations, programming language. Sincetheequivalence of neural networks, etc.Itisalsoa basictheory of deterministic finite automaton (DFA)and noncompiling routine fordiscriminating wordsofa deterministic finite automaton (NFA)inthecapability of programming language. Thispaperanalyses the accepting a programming language wasproved, the equivalence theorem between finite automata and finite automaton became thebasic theory ofdescribing regular expressions, points outtheproblem existing in lexical rules. Stephen Kleene wasthepioneer ofregular theconstruction rules fromfinite automata toregularexpression research onfinite automata that candenote expressions, andproposes further a construction events ofdelineating neural functions. A lexical formula approach fromfinite automata including multi-nodecanbetransformed toaregular expression. A regular loops toregular expressions. Theusage ofthis theorem expression canalso beconstructed toafinite automaton andtheconstruction process ofregular expressions are whichrecognizes allwordsof it.Theregular expatiated, andtheprinciple ofchoosing loops andtheir expressions andfinite automata havethesame simplification fromfinite automatato regularexpressive power. Totransform regular expressions to expressions arediscussed indetail. deterministic finite automaton, weneedtotransform a regular expression to a non-deterministic finite