Displaying similar documents to “Binary operations on automatic functions”

Binary operations on automatic functions

Juhani Karhumäki, Jarkko Kari, Joachim Kupke (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Real functions on the domain [ 0 , 1 ) n – often used to describe digital images – allow for different well-known types of binary operations. In this note, we recapitulate how weighted finite automata can be used in order to represent those functions and how certain binary operations are reflected in the theory of these automata. Different types of products of automata are employed, including the seldomly-used full cartesian product. We show, however, the infeasibility of functional composition;...

Distance desert automata and the star height problem

Daniel Kirsten (2010)

RAIRO - Theoretical Informatics and Applications

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We introduce the notion of nested distance desert automata as a joint generalization of distance automata and desert automata. We show that limitedness of nested distance desert automata is PSPACE-complete. As an application, we show that it is decidable in 2 space whether the language accepted by an -state non-deterministic automaton is of a star height less than a given integer (concerning rational expressions with union, concatenation and iteration), which is the first ever complexity...

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...

Universality of Reversible Hexagonal Cellular Automata

Kenichi Morita, Maurice Margenstern, Katsunobu Imai (2010)

RAIRO - Theoretical Informatics and Applications

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We define a kind of cellular automaton called a hexagonal partitioned cellular automaton (HPCA), and study logical universality of a reversible HPCA. We give a specific 64-state reversible HPCA , and show that a Fredkin gate can be embedded in this cellular space. Since a Fredkin gate is known to be a universal logic element, logical universality of is concluded. Although the number of states of is greater than those of the previous...

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...

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...