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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02 Sep 2014TL;DR: In this article, ND-LTL, an extension of LTL by a restricted form of tuple-navigation, is introduced and studied as an intermediate model simplifying the constructions.
Abstract: We study temporal logics and automata on multi-attributed data words. Recently, BD-LTL was introduced as a temporal logic on data words extending LTL by navigation along positions of single data values. As allowing for navigation wrt. tuples of data values renders the logic undecidable, we introduce ND-LTL, an extension of BD-LTL by a restricted form of tuple-navigation. While complete ND-LTL is still undecidable, the two natural fragments allowing for either future or past navigation along data values are shown to be Ackermann-hard, yet decidability is obtained by reduction to nested multi-counter systems. To this end, we introduce and study nested variants of data automata as an intermediate model simplifying the constructions. To complement these results we show that imposing the same restrictions on BD-LTL yields two 2ExpSpace-complete fragments while satisfiability for the full logic is known to be as hard as reachability in Petri nets.
23 citations
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02 Jun 1997TL;DR: The problem of decidability of the first order theory of one-step rewriting was stated in [CCD93] and in 1995 Ralf Treinen proved that the theory is undecidable.
Abstract: The problem of decidability of the first order theory of one-step rewriting was stated in [CCD93]. One can find the problem on the lists of open problems in rewriting in [DJK93] and [DJK95]. In 1995 Ralf Treinen proved that the theory is undecidable.
23 citations
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17 Jun 2009TL;DR: In this article, the authors tour a fragment of the literature on complexity issues on multi-head automata and show that their computational behavior can lead to undecidableor even non-semi-decidable problems on these devices such as emptiness, uniqueness, universality, equivalence, etc.
Abstract: Multi-head finite automata were introduced in [36] and [38] Since that time, a vast literature oncomputational and descriptional complexity issues on multi-head finite automata documenting theimportance of these devices has been developed Although multi-head finite automata are a sim-ple concept, their computational behavior can be already very complex and leads to undecidableor even non-semi-decidable problems on these devices such as, for example, emptiness, finiteness,universality, equivalence, etc These strong negative results trigger the study of subclasses and al-ternative characterizations of multi-head finite automata for a better understanding of the nature ofnon-recursive trade-offs and, thus, the borderline between decidable and undecidable problems Inthe present paper, we tour a fragment of this literature
23 citations
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27 Jul 1996TL;DR: It is shown that there is no algorithm deciding the ∃*∀*-fragment of this first-order theory of one-step rewriting for an arbitrary rewrite system.
Abstract: The theory of one-step rewriting for a given rewrite system R and signature e is the first-order theory of the following structure: Its universe consists of all e-ground terms, and its only predicate is the relation “x rewrites to y in one step by R”. The structure contains no function symbols and no equality. We show that there is no algorithm deciding the ∃*∀*-fragment of this theory for an arbitrary rewrite system. The proof uses both non-linear and non-shallow rewrite rules.
23 citations
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TL;DR: This survey states some old and new solved and unsolved problems on quantum mechanics, some of which turned out to be undecidable.
23 citations