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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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Proceedings ArticleDOI
05 Dec 1989
TL;DR: A study is made of the real-time performance of a class of rule-based programs written in the language EQL and a general analysis strategy which seems to be quite effective in practical cases is proposed.
Abstract: A study is made of the real-time performance of a class of rule-based programs written in the language EQL. Response time is defined in terms of the computation paths of a program leading to fixed points; investigated is the complexity of the problem of analyzing these programs to meet response-time requirements. It is shown that the response-time analysis problem is in general undecidable and is PSPACE-hard in the case where all the variables have finite domains. A general analysis strategy which seems to be quite effective in practical cases is proposed. This strategy aims at avoiding the combinatorial state-space explosion problem inherent in brute-force approaches. Based on this strategy, a suite of analysis tools has been implemented to verify that the variables in an EQL program always converge to stable values in bounded time. The tools have been successfully applied to real-life programs. >

18 citations

Posted Content
TL;DR: In this article, it was shown that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this remains undecidable among the fundamental groups of compact, non-positively curved square complexes.
Abstract: We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this remains undecidable among the fundamental groups of compact, non-positively curved square complexes. We deduce that many other properties of groups are undecidable. For hyperbolic groups, there cannot exist algorithms to determine largeness, the existence of a linear representation with infinite image (over any infinite field), or the rank of the profinite completion.

18 citations

Journal ArticleDOI
TL;DR: One-Goal Strategy Logic (SL[1G] as mentioned in this paper is a syntactic fragment of SL, which encompasses formulas in prenex normal form having a single temporal goal at a time, for every strategy quantification of agents.
Abstract: Strategy Logic (SL, for short) has been introduced by Mogavero, Murano, and Vardi as a useful formalism for reasoning explicitly about strategies, as first-order objects, in multi-agent concurrent games. This logic turns out to be very powerful, subsuming all major previously studied modal logics for strategic reasoning, including ATL, ATL*, and the like. Unfortunately, due to its high expressiveness, SL has a non-elementarily decidable model-checking problem and the satisfiability question is undecidable, specifically Sigma_1^1. In order to obtain a decidable sublogic, we introduce and study here One-Goal Strategy Logic (SL[1G], for short). This is a syntactic fragment of SL, strictly subsuming ATL*, which encompasses formulas in prenex normal form having a single temporal goal at a time, for every strategy quantification of agents. We prove that, unlike SL, SL[1G] has the bounded tree-model property and its satisfiability problem is decidable in 2ExpTime, thus not harder than the one for ATL*.

18 citations

Journal ArticleDOI
TL;DR: The focus of the paper is on proving the existence of two Special Forms and determining tight response time upper bounds of EQL rule-based programs and how the General Analysis Algorithm can be used with these algorithms.
Abstract: Real-time rule-based expert systems are embedded decision systems that must respond to changes in the environments within stringent timing constraints. Given a program p, the response time analysis problem is to determine the response time of p. This problem consists of: determining whether or not the execution of p always terminates in bounded time; and computing the maximal execution time of p. The Equational Logic (EQL) language is a simple language designed for real-time applications. It has been proved by A.K. Mok (1989) that the response time analysis problem is undecidable if the program variables have infinite domains, and is PSPACE-hard in the case where all of the variables have finite domains. However, we have observed that the use of a simple syntactic and semantic check on programs coupled with other techniques such as state space graph checks can dramatically reduce the time needed in the analysis. There are sets of syntactic and semantic constraint assertions such that if the set S of rules satisfies any of them, then the execution of S always terminates in bounded time. Each of these sets of syntactic and semantic constraint assertions is called a Special Form. The focus of the paper is on proving the existence of two Special Forms and determining tight response time upper bounds of EQL rule-based programs. For each known Special Form, an algorithm used to calculate the maximal response time of programs satisfying this Special Form is presented. Additionally, to enhance the applicability of the proposed algorithms, we show how the General Analysis Algorithm can be used with these algorithms. >

18 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that satisfiability for SPARQL 1.0 patterns is undecidable in general, since the relational algebra can be emulated using such patterns.
Abstract: The satisfiability problem for SPARQL 1.0 patterns is undecidable in general, since the relational algebra can be emulated using such patterns. The goal of this paper is to delineate the boundary of decidability of satisfiability in terms of the constraints allowed in filter conditions. The classes of constraints considered are bound-constraints, negated bound-constraints, equalities, nonequalities, constant-equalities, and constant-nonequalities. The main result of the paper can be summarized by saying that, as soon as inconsistent filter conditions can be formed, satisfiability is undecidable. The key insight in each case is to find a way to emulate the set difference operation. Undecidability can then be obtained from a known undecidability result for the algebra of binary relations with union, composition, and set difference. When no inconsistent filter conditions can be formed, satisfiability is decidable by syntactic checks on bound variables and on the use of literals. Although the problem is shown to be NP-complete, it is experimentally shown that the checks can be implemented efficiently in practice. The paper also points out that satisfiability for the so-called 'well-designed' patterns can be decided by a check on bound variables and a check for inconsistent filter conditions.

18 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023119
2022220
2021120
2020147
2019134
2018136