Journal ArticleDOI
Two-way counter machines and finite-state transducers†
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In this paper, the equivalence problem for deterministic two-way finite-state automata augmented by a bounded-reversal counter was shown to be decidable in general.Abstract:
Consider the emptiness problem for deterministic two-way finite-state automata that are augmented by a bounded-reversal counter and the equivalence problem for deterministic two-way finite-state transducers. The first problem was posed by Ibarra while the second problem restricted to the case that accepting configurations are also halting configurations was posed by Ehrich and Yau. Recently the first problem restricted to devices that accept only bounded languages as well as the restricted version of the second problem have been shown decidable. Here these two problems are shown decidable also in their general form.read more
Citations
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Book ChapterDOI
The Equivalence of Finite Valued Transducers (on HDTOL Languages) is Decidable
Karel Culik,Juhani Karhumäki +1 more
TL;DR: This work shows a generalization of the Ehrenfeucht Conjecture: For every language there exists a (finite) test set with respect to normalized k-valued finite transducers with bounded number of states and shows that for each HDTOL language such a test set can be found effectively.
Journal ArticleDOI
On some transducer equivalence problems for families of languages
TL;DR: In this article, the equivalence and length equivalence of compositions of a morphism and an inverse morphism are studied. But the equivalences of morphisms and their inverses are not considered.
The equivalence of mappings on languages
TL;DR: In this paper, the notion of universal equivalence of mappings on languages has been defined in three different ways and called universal, existential and multiplicative equivalence with multiplicities.
Book ChapterDOI
The equivalence of mappings on languages
TL;DR: This work defines the notion of the equivalence of mappings on languages in three different ways and calls them universal equivalence, existential equivalence and equivalence with multiplicities.
Journal ArticleDOI
Transducing reversibly with finite state machines
TL;DR: Finite state machines are investigated towards their ability to reversibly compute transductions, that is, to transform inputs into outputs in a reversible way, and an infinite and dense hierarchy with respect to the grade of reversibility is obtained.
References
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Journal ArticleDOI
Finite automata and their decision problems
Michael O. Rabin,Dana Scott +1 more
TL;DR: Finite automata are considered as instruments for classifying finite tapes as well as generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined.
Journal ArticleDOI
Reversal-Bounded Multicounter Machines and Their Decision Problems
TL;DR: It is shown that the emptiness, infiniteness, dlsjointness, containment, universe, and equivalence problems are decidable for the class of deterministic two-way multlcounter machines whose input and counters are reversal-bounded.
Journal ArticleDOI
Reversal-bounded multipushdown machines
Brenda S. Baker,Ronald V. Book +1 more
TL;DR: Several representations of the recursively enumerable (r.e.) sets are presented and it is shown that this automata theoretic representation cannot be strengthened by restricting the acceptors to be deterministic multitape, nondeterministic one-tape, or nondetergetic multicounter acceptors.
Journal ArticleDOI
The Diophantine problem for addition and divisibility
TL;DR: In this paper, an algorithm for deciding existential formulas involving addition and the divisibility relation over the natural numbers is given, and the algorithm is shown to be efficient in some cases.