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Manfred Droste - One of the best experts on this subject based on the ideXlab platform.

  • greibach normal form for omega algebraic systems and weighted simple omega pushdown automata
    Foundations of Software Technology and Theoretical Computer Science, 2019
    Co-Authors: Manfred Droste, Sven Dziadek, Werner Kuich
    Abstract:

    In weighted automata theory, many classical results on formal Languages have been extended into a quantitative setting. Here, we investigate weighted Context-Free Languages of infinite words, a generalization of omega-Context-Free Languages (Cohen, Gold 1977) and an extension of weighted Context-Free Languages of finite words (Chomsky, Schutzenberger 1963). As in the theory of formal grammars, these weighted Languages, or omega-algebraic series, can be represented as solutions of mixed omega-algebraic systems of equations and by weighted omega-pushdown automata. In our first main result, we show that mixed omega-algebraic systems can be transformed into Greibach normal form. Our second main result proves that simple omega-reset pushdown automata recognize all omega-algebraic series that are a solution of an omega-algebraic system in Greibach normal form. Simple reset automata do not use epsilon-transitions and can change the stack only by at most one symbol. These results generalize fundamental properties of Context-Free Languages to weighted Languages.

  • the chomsky schutzenberger theorem for quantitative Context Free Languages
    International Journal of Foundations of Computer Science, 2014
    Co-Authors: Manfred Droste, Heiko Vogler
    Abstract:

    Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations like average have been considered. Here, we investigate quantitative Context-Free Languages over very general weight structures incorporating all semirings, average computations, lattices. In our main result, we derive the Chomsky-Schutzenberger Theorem for such quantitative Context-Free Languages, showing that each arises as the image of the intersection of a Dyck language and a recognizable language under a suitable morphism. Moreover, we show that quantitative Context-Free Languages are expressively equivalent to a model of weighted pushdown automata. This generalizes results previously known only for semirings. We also investigate under which conditions quantitative Context-Free Languages assume only finitely many values.

  • the chomsky schutzenberger theorem for quantitative Context Free Languages
    Developments in Language Theory, 2013
    Co-Authors: Manfred Droste, Heiko Vogler
    Abstract:

    Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations like average have been considered. Here, we investigate quantitative Context-Free Languages over very general weight structures incorporating all semirings, average computations, lattices. In our main result, we derive the Chomsky-Schutzenberger Theorem for such quantitative Context-Free Languages, showing that each arises as the image of the intersection of a Dyck language and a recognizable language under a suitable morphism. Moreover, we show that quantitative Context-Free Languages are expressively equivalent to a model of weighted pushdown automata. This generalizes results previously known only for semirings.

Alexander Okhotin - One of the best experts on this subject based on the ideXlab platform.

  • homomorphisms preserving deterministic Context Free Languages
    International Journal of Foundations of Computer Science, 2013
    Co-Authors: Tommi Lehtinen, Alexander Okhotin
    Abstract:

    The paper characterizes the family of homomorphisms, under which the deterministic Context-Free Languages, the LL Context-Free Languages and the unambiguous Context-Free Languages are closed. The f...

  • homomorphisms preserving deterministic Context Free Languages
    Developments in Language Theory, 2012
    Co-Authors: Tommi Lehtinen, Alexander Okhotin
    Abstract:

    The paper characterizes the family of homomorphisms, under which the deterministic Context-Free Languages, the LL Context-Free Languages and the unambiguous Context-Free Languages are closed. The family of deterministic Context-Free Languages is closed under a homomorphism h if and only if h is either a code of bounded deciphering delay, or the images of all symbols under h are powers of the same string. The same characterization holds for LL Context-Free Languages. The unambiguous Context-Free Languages are closed under h if and only if either h is a code, or the images of all symbols under h are powers of the same string.

  • comparing linear conjunctive Languages to subfamilies of the Context Free Languages
    Conference on Current Trends in Theory and Practice of Informatics, 2011
    Co-Authors: Alexander Okhotin
    Abstract:

    Linear conjunctive grammars define the same family of Languages as one-way real-time cellular automata (Okhotin, "On the equivalence of linear conjunctive grammars to trellis automata", RAIRO ITA, 2004), and this family is known to be incomparable to the Context-Free Languages (Terrier, "On real-time one-way cellular array", Theoret. Comput. Sci., 1995). This paper investigates subclasses of the Context-Free Languages for possible containment in this class. It is shown that every visibly pushdown automaton (Alur, Madhusudan, "Visibly pushdown Languages", STOC 2004) can be simulated by a one-way real-time cellular automaton, but already for LL(1) Context-Free Languages and for one-counter DPDAs no simulation is possible.

Heiko Vogler - One of the best experts on this subject based on the ideXlab platform.

  • the chomsky schutzenberger theorem for quantitative Context Free Languages
    International Journal of Foundations of Computer Science, 2014
    Co-Authors: Manfred Droste, Heiko Vogler
    Abstract:

    Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations like average have been considered. Here, we investigate quantitative Context-Free Languages over very general weight structures incorporating all semirings, average computations, lattices. In our main result, we derive the Chomsky-Schutzenberger Theorem for such quantitative Context-Free Languages, showing that each arises as the image of the intersection of a Dyck language and a recognizable language under a suitable morphism. Moreover, we show that quantitative Context-Free Languages are expressively equivalent to a model of weighted pushdown automata. This generalizes results previously known only for semirings. We also investigate under which conditions quantitative Context-Free Languages assume only finitely many values.

  • the chomsky schutzenberger theorem for quantitative Context Free Languages
    Developments in Language Theory, 2013
    Co-Authors: Manfred Droste, Heiko Vogler
    Abstract:

    Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations like average have been considered. Here, we investigate quantitative Context-Free Languages over very general weight structures incorporating all semirings, average computations, lattices. In our main result, we derive the Chomsky-Schutzenberger Theorem for such quantitative Context-Free Languages, showing that each arises as the image of the intersection of a Dyck language and a recognizable language under a suitable morphism. Moreover, we show that quantitative Context-Free Languages are expressively equivalent to a model of weighted pushdown automata. This generalizes results previously known only for semirings.

Werner Kuich - One of the best experts on this subject based on the ideXlab platform.

  • greibach normal form for omega algebraic systems and weighted simple omega pushdown automata
    Foundations of Software Technology and Theoretical Computer Science, 2019
    Co-Authors: Manfred Droste, Sven Dziadek, Werner Kuich
    Abstract:

    In weighted automata theory, many classical results on formal Languages have been extended into a quantitative setting. Here, we investigate weighted Context-Free Languages of infinite words, a generalization of omega-Context-Free Languages (Cohen, Gold 1977) and an extension of weighted Context-Free Languages of finite words (Chomsky, Schutzenberger 1963). As in the theory of formal grammars, these weighted Languages, or omega-algebraic series, can be represented as solutions of mixed omega-algebraic systems of equations and by weighted omega-pushdown automata. In our first main result, we show that mixed omega-algebraic systems can be transformed into Greibach normal form. Our second main result proves that simple omega-reset pushdown automata recognize all omega-algebraic series that are a solution of an omega-algebraic system in Greibach normal form. Simple reset automata do not use epsilon-transitions and can change the stack only by at most one symbol. These results generalize fundamental properties of Context-Free Languages to weighted Languages.

  • a semiring semimodule generalization of ω Context Free Languages
    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2004
    Co-Authors: Zoltán Ésik, Werner Kuich
    Abstract:

    We develop an algebraic theory on semiring-semimodule pairs for ω-Context-Free Languages. We define ω-algebraic systems and characterize their solutions of order k by behaviors of algebraic finite automata. These solutions are then set in correspondence to ω-Context-Free Languages.

Tommi Lehtinen - One of the best experts on this subject based on the ideXlab platform.

  • homomorphisms preserving deterministic Context Free Languages
    International Journal of Foundations of Computer Science, 2013
    Co-Authors: Tommi Lehtinen, Alexander Okhotin
    Abstract:

    The paper characterizes the family of homomorphisms, under which the deterministic Context-Free Languages, the LL Context-Free Languages and the unambiguous Context-Free Languages are closed. The f...

  • homomorphisms preserving deterministic Context Free Languages
    Developments in Language Theory, 2012
    Co-Authors: Tommi Lehtinen, Alexander Okhotin
    Abstract:

    The paper characterizes the family of homomorphisms, under which the deterministic Context-Free Languages, the LL Context-Free Languages and the unambiguous Context-Free Languages are closed. The family of deterministic Context-Free Languages is closed under a homomorphism h if and only if h is either a code of bounded deciphering delay, or the images of all symbols under h are powers of the same string. The same characterization holds for LL Context-Free Languages. The unambiguous Context-Free Languages are closed under h if and only if either h is a code, or the images of all symbols under h are powers of the same string.