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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19 Aug 2008TL;DR: It is shown that the existence of a terminating computation is decidable, but that termination with any probability strictly greater than zero is undecidable, and that the fairness intrinsic in stochastic computations implies that termination of all computation paths is Undecidable.
Abstract: We consider nondeterministic and probabilistic termination problems in a process algebra that is equivalent to basic chemistry. We show that the existence of a terminating computation is decidable, but that termination with any probability strictly greater than zero is undecidable. Moreover, we show that the fairness intrinsic in stochastic computations implies that termination of all computation paths is undecidable, while it is decidable in a nondeterministic framework.
35 citations
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18 Jul 2021TL;DR: In this paper, an asynchronous variant of HyperLTL has been proposed, where traces can take stuttering steps independently, and the model-checking problem for this variant is undecidable.
Abstract: Hyperproperties are properties of computational systems that require more than one trace to evaluate, e.g., many information-flow security and concurrency requirements. Where a trace property defines a set of traces, a hyperproperty defines a set of sets of traces. The temporal logics HyperLTL and HyperCTL* have been proposed to express hyperproperties. However, their semantics are synchronous in the sense that all traces proceed at the same speed and are evaluated at the same position. This precludes the use of these logics to analyze systems whose traces can proceed at different speeds and allow that different traces take stuttering steps independently. To solve this problem in this paper, we propose an asynchronous variant of HyperLTL. On the negative side, we show that the model-checking problem for this variant is undecidable. On the positive side, we identify a decidable fragment which covers a rich set of formulas with practical applications. We also propose two model-checking algorithms that reduce our problem to the HyperLTL model-checking problem in the synchronous semantics.
35 citations
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TL;DR: The following four properties are shown undecidable for finite Thue systems S: Is S equivalent to a finite Church-Rosser (respectively: almost confluent, preperfect) system?
35 citations
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TL;DR: In this article, it was shown that every polynomial-time predicate can be defined by an (unstratified) local rule set, and a new machine-recognizable subclass of the local rule sets is identified.
Abstract: We consider the concept of a local set of inference rules. A local rule set can be automatically transformed into a rule set for which bottom-up evaluation terminates in polynomial time. The local-rule-set transformation gives polynomial-time evaluation strategies for a large variety of rule sets that cannot be given terminating evaluation strategies by any other known automatic technique. This article discusses three new results. First, it is shown that every polynomial-time predicate can be defined by an (unstratified) local rule set. Second, a new machine-recognizable subclass of the local rule sets is identified. Finally, we show that locality, as a property of rule sets, is undecidable in general.
35 citations
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TL;DR: Algorithms of lower complexity are obtained for solving the problem of whether or not a given finite string-rewriting system R is confluent on a given congruence class [w]R, when only length-reducing systems are considered.
35 citations