Displaying similar documents to “Relating Automata-theoretic Hierarchies to Complexity-theoretic Hierarchies”

Relating automata-theoretic hierarchies to complexity-theoretic hierarchies

Victor L. Selivanov (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We show that some natural refinements of the Straubing and Brzozowski hierarchies correspond (via the so called leaf-languages) step by step to similar refinements of the polynomial-time hierarchy. This extends a result of Burtschik and Vollmer on relationship between the Straubing and the polynomial hierarchies. In particular, this applies to the Boolean hierarchy and the plus-hierarchy.

On Existentially First-Order Definable Languages and Their Relation to NP

Bernd Borchert, Dietrich Kuske, Frank Stephan (2010)

RAIRO - Theoretical Informatics and Applications

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Under the assumption that the Polynomial-Time Hierarchy does not collapse we show for a regular language : the unbalanced polynomial-time leaf language class determined by equals  iff is existentially but not quantifierfree definable in FO[<, min, max, +1, −1]. Furthermore, no such class lies properly between NP and co-1-NP or NP⊕co-NP. The proofs rely on a result of Pin and Weil characterizing the automata of existentially first-order definable languages.

k-counting automata

Joël Allred, Ulrich Ultes-Nitsche (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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In this paper, we define -counting automata as recognizers for -languages, languages of infinite words. We prove that the class of -languages they recognize is a proper extension of the -regular languages. In addition we prove that languages recognized by -counting automata are closed under Boolean operations. It remains an open problem whether or not emptiness is decidable for -counting automata. However, we conjecture strongly that it is decidable and give formal reasons why we believe...

On the classes of languages accepted by limited context restarting automata

Friedrich Otto, Peter Černo, František Mráz (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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In the literature various types of restarting automata have been studied that are based on contextual rewriting. A word is accepted by such an automaton if, starting from the initial configuration that corresponds to input , the word is reduced to the empty word by a finite number of applications of these contextual rewritings. This approach is reminiscent of the notion of McNaughton families of languages. Here we put the aforementioned types of restarting automata into the context...

Hyper-minimizing minimized deterministic finite state automata

Andrew Badr, Viliam Geffert, Ian Shipman (2007)

RAIRO - Theoretical Informatics and Applications

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We present the first (polynomial-time) algorithm for reducing a given deterministic finite state automaton (DFA) into a DFA, which may have fewer states than the classically minimized DFA. The price we pay is that the language recognized by the new machine can differ from the original on a finite number of inputs. These hyper-minimized automata are optimal, in the sense that every DFA with fewer states must disagree on infinitely many inputs. With small modifications, the construction...

-counting automata

Joël Allred, Ulrich Ultes-Nitsche (2012)

RAIRO - Theoretical Informatics and Applications

Similarity:

In this paper, we define -counting automata as recognizers for -languages, languages of infinite words. We prove that the class of -languages they recognize is a proper extension of the -regular languages. In addition we prove that languages recognized by -counting automata are closed under Boolean operations. It remains an open problem whether or not emptiness is decidable for -counting automata. However, we conjecture strongly...