Topic
Undecidable problem
About: Undecidable problem is a research topic. Over the lifetime, 3135 publications have been published within this topic receiving 71238 citations.
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30 Aug 1999
TL;DR: It is shown that this class of graphs associated to linear bounded machines is closed, up to observational equivalence, under synchronized product, and the first-order theory of these graphs is investegated and shown to be undecidable.
Abstract: This paper introduces a class of graphs associated to linear bounded machines It is shown that this class is closed, up to observational equivalence, under synchronized product The first-order theory of these graphs is investegated and shown to be undecidable The latter result extends to any logic in which the existence of sinks may be stated
15 citations
TL;DR: It is shown that the membership problems for RAGs and for context-free array grammars (CFAG) are both NP-complete.
15 citations
01 Jan 1987
TL;DR: A general method by which various natural decision problems for programs in PROLOG and extensions of PROLOG can easily be shown to be recursively unsolvable is presented.
Abstract: The paper presents a general method by which various natural decision problems for programs in PROLOG and extensions of PROLOG can easily be shown to be recursively unsolvable. A particularly interesting application of this method gives an affirmative answer to Flannagan's [1985] conjecture that the floundering property for queries with respect to MU-PROLOG programs is undecidable.
15 citations
Posted Content•
TL;DR: In this paper, the authors consider generalized energy games on infinite game graphs induced by pushdown automata (modeling recursion) or their subclass of one-counter automata and show that energy games are decidable in the case where the game graph is induced by a one-Counter automaton and the energy is one-dimensional.
Abstract: Energy games are a well-studied class of 2-player turn-based games on a finite graph where transitions are labeled with integer vectors which represent changes in a multidimensional resource (the energy). One player tries to keep the cumulative changes non-negative in every component while the other tries to frustrate this. We consider generalized energy games played on infinite game graphs induced by pushdown automata (modelling recursion) or their subclass of one-counter automata. Our main result is that energy games are decidable in the case where the game graph is induced by a one-counter automaton and the energy is one-dimensional. On the other hand, every further generalization is undecidable: Energy games on one-counter automata with a 2-dimensional energy are undecidable, and energy games on pushdown automata are undecidable even if the energy is one-dimensional. Furthermore, we show that energy games and simulation games are inter-reducible, and thus we additionally obtain several new (un)decidability results for the problem of checking simulation preorder between pushdown automata and vector addition systems.
15 citations
24 Mar 2012
TL;DR: It is shown that model checking EF logic on POCA without parameters is PSPACE-complete, and the PSPACE upper bound is obtained by analysing systems of linear Diophantine inequalities of exponential size that admit solutions of polynomial size.
Abstract: We study the computational complexity of model checking EF logic and modal logic on parametric one-counter automata (POCA). A POCA is a one-counter automaton whose counter updates are either integer values encoded in binary or integer-valued parameters. Given a formula and a configuration of a POCA, the model-checking problem asks whether the formula is true in this configuration for all possible valuations of the parameters. We show that this problem is undecidable for EF logic via reduction from Hilbert's tenth problem, however for modal logic we prove PSPACE-completeness. Obtaining the PSPACE upper bound involves analysing systems of linear Diophantine inequalities of exponential size that admit solutions of polynomial size. Finally, we show that model checking EF logic on POCA without parameters is PSPACE-complete.
15 citations