Formal Reductions of the General Combinatorial Decision Problem

Post, Emil L.

doi:10.2307/2371809

Cited by 636 publications

(233 citation statements)

References 0 publications

Supporting

Mentioning

221

Contrasting

Unclassified

Order By: Relevance

“…The notion that rewriting words (or terms) can be a basis for defining computability goes back to the works of Axel Thue [22] (Thue systems) and Emil Post [17] (Post's tag systems). Formal languages defined using grammars (the Chomsky hierarchy) are also in the spirit of rewriting, with semi-Thue systems corresponding to unrestricted grammars and hence Turing machines.…”

Section: Introductionmentioning

confidence: 99%

An Infinite Automaton Characterization of Double Exponential Time

Torre

Madhusudan

Parlato

2008

Computer Science Logic

View full text Add to dashboard Cite

Abstract. Infinite-state automata are a new invention: they are automata that have an infinite number of states represented by words, transitions defined using rewriting, and with sets of initial and final states. Infinite-state automata have gained recent interest due to a remarkable result by Morvan and Stirling, which shows that automata with transitions defined using rational rewriting precisely capture context-sensitive (NLINSPACE) languages. In this paper, we show that infinite automata defined using a form of multi-stack rewriting precisely defines double exponential time (more precisely, 2ETIME, the class of problems solvable in 2 2 O(n) time). The salient aspect of this characterization is that the automata have no ostensible limits on time nor space, and neither direction of containment with respect to 2ETIME is obvious. In this sense, the result captures the complexity class qualitatively, by restricting the power of rewriting.

show abstract

Section: Introductionmentioning

confidence: 99%

An Infinite Automaton Characterization of Double Exponential Time

Torre

Madhusudan

Parlato

2008

Computer Science Logic

View full text Add to dashboard Cite

show abstract

“…The idea of representing knowledge in the form of products appeared in the work of Emil Leon Post (Post, 1943).…”

Section: Fig 7 Structure Of the Esmentioning

confidence: 99%

Ontology Approach in Lens Design

Livshits¹,

Mouromtsev²,

Vasiliev³

2012

Modern Information Systems

View full text Add to dashboard Cite

“…A Post system (Post (1943)) is a formal logical system 11 A recursively enumerable set can be defined as a set whose partial characteristic function is computable or, equivalently, as the range of some computable function (see e.g. Cutland (1980) or Cohen (1987)).…”

Section: -Rational Vs Norm-guided Behaviourmentioning

confidence: 99%