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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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Book ChapterDOI
02 Nov 2020
TL;DR: This paper provides a translation to a new first-order language, called SCL, that precisely captures the semantics of SHACL w.r.t. satisfiability and containment and provides the detailed map of decidability and complexity results of the aforementioned decision problems for differentSHACL sublanguages.
Abstract: The Shapes Constraint Language (SHACL) is a recent W3C recommendation language for validating RDF data. Specifically, SHACL documents are collections of constraints that enforce particular shapes on an RDF graph. Previous work on the topic has provided theoretical and practical results for the validation problem, but did not consider the standard decision problems of satisfiability and containment, which are crucial for verifying the feasibility of the constraints and important for design and optimization purposes. In this paper, we undertake a thorough study of the different features of SHACL by providing a translation to a new first-order language, called Open image in new window , that precisely captures the semantics of SHACL w.r.t. satisfiability and containment. We study the interaction of SHACL features in this logic and provide the detailed map of decidability and complexity results of the aforementioned decision problems for different SHACL sublanguages. Notably, we prove that both problems are undecidable for the full language, but we present decidable combinations of interesting features.

15 citations

Proceedings Article
02 Aug 2001
TL;DR: In this article, an extension to the traditional λ-calculus as a framework for families of Turing complete stochastic languages is presented, and a class of exact inference algorithms based on the traditional reductions of the λ calculus is presented.
Abstract: There is increasing interest within the research community in the design and use of recursive probability models. There remains concern about computational complexity costs and the fact that computing exact solutions can be intractable for many nonrecursive models. Although inference is undecidable in the general case for recursive problems, several research groups are actively developing computational techniques for recursive stochastic languages. We have developed an extension to the traditional λ calculus as a framework for families of Turing complete stochastic languages. We have also developed a class of exact inference algorithms based on the traditional reductions of the λ calculus. We further propose that using the deBruijn notation (a λ-calculus notation with nameless dummies) supports effective caching in such systems, as the reuse of partial solutions is an essential component of efficient computation. Finally, our extension to the λ-calculus offers a foundation and general theory for the construction of recursive stochastic modeling languages as well as promise for effective caching and efficient approximation algorithms for inference.

15 citations

Journal ArticleDOI
TL;DR: The problem whether there exists a unifying substitution for two terms is considered in the class of theories which can be embedded into canonical term rewriting systems and the problem is shown to be undecidable, even if the authors restrict the substitutions to matching ones.
Abstract: The problem whether there exists a unifying substitution for two terms is considered in the class of theories which can be embedded into canonical term rewriting systems. The problem is shown to be undecidable, even if we restrict the substitutions to matching ones. This implies that the class of admissible canonical theories is a proper subset of the class of canonical theories.

15 citations

Book ChapterDOI
20 May 2008
TL;DR: This paper extends the algorithm for SSMT for decidable theories presented in [FHT08] to non-linear arithmetic theories over the reals and integers which are in general undecidable which permits the concise description of diverse problems combining reasoning under uncertainty with data dependencies.
Abstract: The stochastic satisfiability modulo theories (SSMT) problem is a generalization of the SMT problem on existential and randomized (aka stochastic) quantification over discrete variables of an SMT formula This extension permits the concise description of diverse problems combining reasoning under uncertainty with data dependencies Solving problems with various kinds of uncertainty has been extensively studied in Artificial Intelligence Famous examples are stochastic satisfiability and stochastic constraint programming In this paper, we extend the algorithm for SSMT for decidable theories presented in [FHT08] to non-linear arithmetic theories over the reals and integers which are in general undecidable Therefore, we combine approaches from Constraint Programming, namely the iSAT algorithm tackling mixed Boolean and non-linear arithmetic constraint systems, and from Artificial Intelligence handling existential and randomized quantifiers Furthermore, we evaluate our novel algorithm and its enhancements on benchmarks from the probabilistic hybrid systems domain

15 citations

Posted Content
TL;DR: This work presents a semi-decision procedure that constructs implementations and counterexamples up to a given bound of HyperLTL, and shows that, while the synthesis problem is undecidable for full HyperL TL, it remains decidable for the \(\exists ^*\), \(\exist ^1\), and the \( linear \;\forall ^*\) fragments.
Abstract: We study the reactive synthesis problem for hyperproperties given as formulas of the temporal logic HyperLTL. Hyperproperties generalize trace properties, i.e., sets of traces, to sets of sets of traces. Typical examples are information-flow policies like noninterference, which stipulate that no sensitive data must leak into the public domain. Such properties cannot be expressed in standard linear or branching-time temporal logics like LTL, CTL, or CTL$^*$. We show that, while the synthesis problem is undecidable for full HyperLTL, it remains decidable for the $\exists^*$, $\exists^*\forall^1$, and the $\mathit{linear}\;\forall^*$ fragments. Beyond these fragments, the synthesis problem immediately becomes undecidable. For universal HyperLTL, we present a semi-decision procedure that constructs implementations and counterexamples up to a given bound. We report encouraging experimental results obtained with a prototype implementation on example specifications with hyperproperties like symmetric responses, secrecy, and information-flow.

15 citations


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