396 research outputs found

    The exact hardness of deciding derivational and runtime complexity

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    For any class C of computable total functions satisfying some mild conditions, we prove that the following decision problems are complete for the existential part of the second level of the arithmetical hierarchy: (A) Deciding whether a term rewriting system (TRS for short) has runtime complexity bounded by a function in C. (B) Deciding whether a TRS has derivational complexity bounded by a function in C. In particular, the problems of deciding whether a TRS has polynomially (exponentially) bounded runtime complexity (respectively derivational complexity) are complete for this level of the arithmetical ierarchy. This places deciding polynomial derivational or runtime complexity of TRSs at the same level as deciding nontermination or nonconfluence of TRSs. We proceed to show that the related problem of deciding for a single computable function f whether a TRS has runtime complexity bounded from above by f is complete for the universal part of the first level of the arithmetical hierarchy. We further prove that analysing the implicit complexity of TRSs is even more difficult: The problem of deciding whether a TRS accepts a language of terms accepted by some TRS with runtime complexity bounded by a function in C is complete for the existential part of the third level of the arithmetical hierarchy. All of our results are easily extended to the notion of minimal complexity (where the length of shortest reductions to normal form is considered) and remain valid under any computable reduction strategy. Finally, all results hold both for unrestricted TRSs and for the class of orthogonal TRSs

    Termination and Productivity

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    Klop, J.W. [Promotor]Vrijer, R.C. de [Copromotor

    Are there new models of computation? Reply to Wegner and Eberbach

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    Wegner and Eberbach[Weg04b] have argued that there are fundamental limitations to Turing Machines as a foundation of computability and that these can be overcome by so-called superTuring models such as interaction machines, the [pi]calculus and the $-calculus. In this paper we contest Weger and Eberbach claims

    Certification of Classical Confluence Results for Left-Linear Term Rewrite Systems

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    Weak Alternating Timed Automata

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    Alternating timed automata on infinite words are considered. The main result is a characterization of acceptance conditions for which the emptiness problem for these automata is decidable. This result implies new decidability results for fragments of timed temporal logics. It is also shown that, unlike for MITL, the characterisation remains the same even if no punctual constraints are allowed

    Relational extensions to feature logic: applications to constraint based grammars

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    This thesis investigates the logical and computational foundations of unification-based or more appropriately constraint based grammars. The thesis explores extensions to feature logics (which provide the basic knowledge representation services to constraint based grammars) with multi-valued or relational features. These extensions are useful for knowledge representation tasks that cannot be expressed within current feature logics.The approach bridges the gap between concept languages (such as KL-ONE), which are the mainstay of knowledge representation languages in AI, and feature logics. Va¬ rious constraints on relational attributes are considered such as existential membership, universal membership, set descriptions, transitive relations and linear precedence con¬ straints.The specific contributions of this thesis can be summarised as follows: 1. Development of an integrated feature/concept logic 2. Development of a constraint logic for so called partial set descriptions 3. Development of a constraint logic for expressing linear precedence constraints 4. The design of a constraint language CL-ONE that incorporates the central ideas provided by the above study 5. A study of the application of CL-ONE for constraint based grammarsThe thesis takes into account current insights in the areas of constraint logic programming, object-oriented languages, computational linguistics and knowledge representation

    Timed Automata Semantics for Analyzing Creol

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    We give a real-time semantics for the concurrent, object-oriented modeling language Creol, by mapping Creol processes to a network of timed automata. We can use our semantics to verify real time properties of Creol objects, in particular to see whether processes can be scheduled correctly and meet their end-to-end deadlines. Real-time Creol can be useful for analyzing, for instance, abstract models of multi-core embedded systems. We show how analysis can be done in Uppaal.Comment: In Proceedings FOCLASA 2010, arXiv:1007.499
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