Results 1  10
of
19
An effective decision procedure for linear arithmetic with integer and real variables
 ACM Transactions on Computational Logic (TOCL
, 2005
"... This article considers finiteautomatabased algorithms for handling linear arithmetic with both real and integer variables. Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this involves some difficult and delicate to implement algorithms. T ..."
Abstract

Cited by 24 (5 self)
 Add to MetaCart
(Show Context)
This article considers finiteautomatabased algorithms for handling linear arithmetic with both real and integer variables. Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this involves some difficult and delicate to implement algorithms. The contribution of this article is to show, using topological arguments, that only a restricted class of automata on infinite words are necessary for handling real and integer linear arithmetic. This allows the use of substantially simpler algorithms, which have been successfully implemented.
On Syntactic Congruences for ωLanguages
 Theoretical Computer Science
, 1997
"... Theoret. Comput. Sci., Vol. 183, No. 1, pp. 93 – 112. This flaw causes subsequent ones ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
Theoret. Comput. Sci., Vol. 183, No. 1, pp. 93 – 112. This flaw causes subsequent ones
HIGHLY UNDECIDABLE PROBLEMS FOR INFINITE COMPUTATIONS
 THEORETICAL INFORMATICS AND APPLICATIONS
, 2009
"... We show that many classical decision problems about 1counter ωlanguages, context free ωlanguages, or infinitary rational relations, are Π 1 2complete, hence located at the second level of the analytical hierarchy, and “highly undecidable”. In particular, the universality problem, the inclusion ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
(Show Context)
We show that many classical decision problems about 1counter ωlanguages, context free ωlanguages, or infinitary rational relations, are Π 1 2complete, hence located at the second level of the analytical hierarchy, and “highly undecidable”. In particular, the universality problem, the inclusion problem, the equivalence problem, the determinizability problem, the complementability problem, and the unambiguity problem are all Π 1 2complete for contextfree ωlanguages or for infinitary rational relations. Topological and arithmetical properties of 1counter ωlanguages, context free ωlanguages, or infinitary rational relations, are also highly undecidable. These very surprising results provide the first examples of highly undecidable problems about the behaviour of very simple finite machines like 1counter automata or 2tape automata.
Efficient Minimization of Deterministic Weak ωAutomata
, 2001
"... We analyze the minimization problem for deterministic weak automata, a subclass of deterministic Büchi automata, which recognize the regular languages that are recognizable by deterministic Büchi and deterministic coBüchi automata. We reduce the problem to the minimization of finite automata on fin ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We analyze the minimization problem for deterministic weak automata, a subclass of deterministic Büchi automata, which recognize the regular languages that are recognizable by deterministic Büchi and deterministic coBüchi automata. We reduce the problem to the minimization of finite automata on finite words and obtain an algorithm running in time O(n log n), where n is the number of states of the automaton.
The Kolmogorov complexity of infinite words
 7TH WORKSHOP ”DESCRIPTIONAL COMPLEXITY OF FORMAL SYSTEMS"
, 2007
"... We present a brief survey of results on relations between the Kolmogorov complexity of infinite strings and several measures of information content (dimensions) known from dimension theory, information theory or fractal geometry. Special emphasis is laid on bounds on the complexity of strings in con ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We present a brief survey of results on relations between the Kolmogorov complexity of infinite strings and several measures of information content (dimensions) known from dimension theory, information theory or fractal geometry. Special emphasis is laid on bounds on the complexity of strings in constructively given subsets of the Cantor space. Finally, we compare the Kolmogorov complexity to the subword complexity of infinite strings.
Borel ranks and Wadge degrees of context free ωlanguages
"... We determine completely the Borel hierarchy of the class of context free ωlanguages, showing that, for each recursive non null ordinal α, there exist some Σ 0 αcomplete and some Π 0 αcomplete ωlanguages accepted by Büchi 1counter automata. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We determine completely the Borel hierarchy of the class of context free ωlanguages, showing that, for each recursive non null ordinal α, there exist some Σ 0 αcomplete and some Π 0 αcomplete ωlanguages accepted by Büchi 1counter automata.
THE COMPLEXITY OF INFINITE COMPUTATIONS IN MODELS OF SET THEORY
, 2009
"... ABSTRACT. We prove the following surprising result: there exist a 1counter Büchi automaton A and a 2tape Büchi automaton B such that: (1) There is a model V1 of ZFC in which the ωlanguage L(A) and the infinitary rational relation L(B) are Π 0 2sets, and (2) There is a model V2 of ZFC in which th ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
ABSTRACT. We prove the following surprising result: there exist a 1counter Büchi automaton A and a 2tape Büchi automaton B such that: (1) There is a model V1 of ZFC in which the ωlanguage L(A) and the infinitary rational relation L(B) are Π 0 2sets, and (2) There is a model V2 of ZFC in which the ωlanguage L(A) and the infinitary rational relation L(B) are analytic but non Borel sets. This shows that the topological complexity of an ωlanguage accepted by a 1counter Büchi automaton or of an infinitary rational relation accepted by a 2tape Büchi automaton is not determined by the axiomatic system ZFC. We show that a similar result holds for the class of languages of infinite pictures which are recognized by Büchi tiling systems. We infer from the proof of the above results an improvement of the lower bound of some decision problems recently studied in [Fin09b, Fin09a]. 1.
Hausdorff Measure and Łukasiewicz Languages
 J. of Universal Computer Science
, 2006
"... The paper investigates fixed points and attractors of infinite iterated function systems in Cantor space. By means of the theory of formal languages simple examples of the noncoincidence of fixed point and attractor (closure of the fixed point) are given. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
The paper investigates fixed points and attractors of infinite iterated function systems in Cantor space. By means of the theory of formal languages simple examples of the noncoincidence of fixed point and attractor (closure of the fixed point) are given.
The Determinacy of ContextFree Games
"... We prove that the determinacy of GaleStewart games whose winning sets are accepted by realtime 1counter Büchi automata is equivalent to the determinacy of (effective) analytic GaleStewart games which is known to be a large cardinal assumption. We show also that the determinacy of Wadge games betw ..."
Abstract
 Add to MetaCart
(Show Context)
We prove that the determinacy of GaleStewart games whose winning sets are accepted by realtime 1counter Büchi automata is equivalent to the determinacy of (effective) analytic GaleStewart games which is known to be a large cardinal assumption. We show also that the determinacy of Wadge games between two players in charge of ωlanguages accepted by 1counter Büchi automata is equivalent to the (effective) analytic Wadge determinacy. Using some results of set theory we prove that one can effectively construct a 1counter Büchi automaton A and a Büchi automaton B such that: (1) There exists a model of ZFC in which Player 2 has a winning strategy in the Wadge game W (L(A), L(B)); (2) There exists a model of ZFC in which the Wadge game W (L(A), L(B)) is not determined. Moreover these are the only two possibilities, i.e. there are no models of ZFC in which Player 1 has a winning strategy in the Wadge game W (L(A), L(B)).