scispace - formally typeset
Search or ask a question
Topic

Undecidable problem

About: Undecidable problem is a research topic. Over the lifetime, 3135 publications have been published within this topic receiving 71238 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: The formal system studied in Lipton is shown to be inadequate for Computer Science in the sense that it has a model with the following defects: finite sets may be undecidable in the model.

29 citations

Proceedings ArticleDOI
02 Aug 2009
TL;DR: This work describes and proves correct a new, terminating constraint simplification algorithm for a dynamic pattern fragment of higher-order unification in a dependent type system, and discusses its implementation.
Abstract: Higher-order unification is undecidable, but has fragments which admit practical algorithms, which are used extensively in logical frameworks. For example, it is decidable whether unification problems in the pattern fragment are solvable, and they enjoy unique most general unifiers when they are.Often we wish to treat more general problems which are nonetheless solvable by incrementally reasoning about the parts of them that fall in the pattern fragment after more progress has been made --- to this end constraint simplification algorithms have been proposed, which work on the so-called dynamic pattern fragment. However, their theory turns out to be surprisingly subtle. The constraint simplification algorithm implemented in Twelf, for instance, is not terminating, despite the sketch of a proof of its termination in the literature. We describe and prove correct a new, terminating constraint simplification algorithm for a dynamic pattern fragment of higher-order unification in a dependent type system, and discuss its implementation.

29 citations

01 Jan 2005
TL;DR: In this paper, the authors present a framework for security protocol analysis that can handle algebraic properties of cryptographic operators in a uniform and modular way, based on the use of modular rewriting to formalize a generalized equational deduction problem for the Dolev- Yao intruder.
Abstract: Many security protocols fundamentally depend on the algebraic properties of cryptographic operators. It is however difficult to handle these properties when formally analyzing protocols, since basic problems like the equality of terms that represent cryptographic messages are undecidable, even for relatively simple algebraic theories. We present a framework for security protocol analysis that can handle algebraic properties of cryptographic operators in a uniform and modular way. Our framework is based on two ideas: the use of modular rewriting to formalize a generalized equational deduction problem for the Dolev- Yao intruder, and the introduction of two parameters that control the complexity of the equational unification problems that arise during protocol analysis by bounding the depth of message terms and the operations that the intruder can perform when analyzing messages.We motivate the different restrictions made in our model by highlighting different ways in which undecidability arises when incorporating algebraic properties of cryptographic operators into formal protocol analysis.

29 citations

Book ChapterDOI
11 Jul 1994
TL;DR: The main result states that every Turing Machine can be realized by a dynamical system with piecewise-constant derivatives in a 3-dimensional space and thus the reachability problem for such systems is undecidable for 3 dimensions.
Abstract: In this paper we define a precise notion of abstraction relation between continuous dynamical systems and discrete state-transition systems. Our main result states that every Turing Machine can be realized by a dynamical system with piecewise-constant derivatives in a 3-dimensional space and thus the reachability problem for such systems is undecidable for 3 dimensions. A decision procedure for 2-dimensional systems has been recently reported by Maler and Pnueli. On the other hand we show that some non-deterministic finite automata cannot be realized by any continuous dynamical system with less than 3 dimensions.

29 citations

Book ChapterDOI
18 Sep 2013
TL;DR: This paper introduces a variant of Golog where basic actions are defined using such a DL-based formalism, and shows that the verification problem for such programs is decidable.
Abstract: High-level action programming languages such as Golog have successfully been used to model the behavior of autonomous agents. In addition to a logic-based action formalism for describing the environment and the effects of basic actions, they enable the construction of complex actions using typical programming language constructs. To ensure that the execution of such complex actions leads to the desired behavior of the agent, one needs to specify the required properties in a formal way, and then verify that these requirements are met by any execution of the program. Due to the expressiveness of the action formalism underlying Golog (Situation Calculus), the verification problem for Golog programs is in general undecidable. Action formalisms based on Description Logic (DL) try to achieve decidability of inference problems such as the projection problem by restricting the expressiveness of the underlying base logic. However, until now these formalisms have not been used within Golog programs. In the present paper, we introduce a variant of Golog where basic actions are defined using such a DL-based formalism, and show that the verification problem for such programs is decidable. This improves on our previous work on verifying properties of infinite sequences of DL actions in that it considers (finite and infinite) sequences of DL actions that correspond to (terminating and non-terminating) runs of a Golog program rather than just infinite sequences accepted by a Buchi automaton abstracting the program.

29 citations


Network Information
Related Topics (5)
Model checking
16.9K papers, 451.6K citations
89% related
Concurrency
13K papers, 347.1K citations
88% related
Logic programming
11.1K papers, 274.2K citations
88% related
Temporal logic
7.6K papers, 262K citations
87% related
Mathematical proof
13.8K papers, 374.4K citations
86% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023119
2022220
2021120
2020147
2019134
2018136