Theory of linear and integer programming
Theory of linear and integer programming
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
The equivalence problem of multitape finite automata
Theoretical Computer Science
On the representation of finite deterministic 2-tape automata
Theoretical Computer Science
Journal of the ACM (JACM)
Reversal-Bounded Multicounter Machines and Their Decision Problems
Journal of the ACM (JACM)
Automata, Languages, and Machines
Automata, Languages, and Machines
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Decision Problems for Semi-Thue Systems with a Few Rules
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Separability of rational relations in A* × Nm by recognizable relations is decidable
Information Processing Letters
An automata theoretic approach to rational tree relations
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
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The definition of the class of deterministic rational relations is fundamentally based on the Read-only One-way Turing machine approach. The notion of deterministic automata developed up to now is too strong and asks for an unnatural detour via end-markers to give all deterministic rational relations (cf. Section 3.1). We stress that several conditions usually considered as related to determinism are mere normalizations of determinism and are not inherent to the notion (cf. Section 3.2). In this paper, we introduce pertinent notions of deterministic labelled graph automata (cf. Section 3.3) which avoid any use of end-markers: strong deterministic, n-deterministic automata for nN. These notions form an increasing infinite hierarchy of classes of automata which all lead to the same usual class of deterministic rational relations. Moreover, the class corresponding to the natural extension to the case n= is exactly the class of unambiguous automata. We also consider Nivat's characterization via multimorphisms applied to rational languages and introduce a hierarchy of deterministic versions of multimorphisms. Properties of determinism and unambiguity are compared. The decision problems for ambiguity or determinism relative to automata and multimorphisms are settled. Roughly, all problems are undecidable in case of arity 2 with at least two non-binary alphabets, else they are decidable, most being even polynomial time decidable.