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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 Article•
25 Jul 2015
TL;DR: The model checking problem for Resource Agent Logic is known to be undecidable as discussed by the authors, but it is known that model checking is decidable for a class of models in which agents always have a choice of doing nothing.
Abstract: The model-checking problem for Resource Agent Logic is known to be undecidable. We review existing (un)decidability results and identify a significant fragment of the logic for which model checking is decidable. We discuss aspects which makes model checking decidable and prove undecidability of two open fragments over a class of models in which agents always have a choice of doing nothing.
15 citations
29 Oct 2015
TL;DR: It is proved that even MLSL without length measurement is undecidable, and the intersection emptiness of two context-free languages to the respective satisfiability problem is reduced.
Abstract: We consider undecidability of Multi-Lane Spatial Logic MLSL, a multi-dimensional modal logic introduced for reasoning about traffic manoeuvres. MLSL with length measurement has been shown to be undecidable. However, the proof relies on exact values. This raises the question whether the logic remains undecidable when we consider robust satisfiability, i.e. when values are known only approximately. Our main result is that robust satisfiability of MLSL is undecidable. Furthermore, we prove that even MLSL without length measurement is undecidable. In both cases we reduce the intersection emptiness of two context-free languages to the respective satisfiability problem.
14 citations
18 Aug 2014
TL;DR: This paper extends earlier results to identify a large, non-trivial fragment of the formalism where verification is decidable of GOLOG, and considers properties expressed in a first-order variant of the branching-time temporal logic CTL*.
Abstract: GOLOG is a high-level action programming language for controlling autonomous agents such as mobile robots. It is defined on top of a logic-based action theory expressed in the Situation Calculus. Before a program is deployed onto an actual robot and executed in the physical world, it is desirable, if not crucial, to verify that it meets certain requirements (typically expressed through temporal formulas) and thus indeed exhibits the desired behaviour. However, due to the high (first-order) expressiveness of the language, the corresponding verification problem is in general undecidable. In this paper, we extend earlier results to identify a large, non-trivial fragment of the formalism where verification is decidable. In particular, we consider properties expressed in a first-order variant of the branching-time temporal logic CTL*. Decidability is obtained by (1) resorting to the decidable first-order fragment C2 as underlying base logic, (2) using a fragment of GOLOG with ground actions only, and (3) requiring the action theory to only admit local effects.
14 citations
01 Jan 2010
TL;DR: It is shown that regular collections of time-constrained MSCs can be translated into a special class of event-clock automata that can be determinized and complemented, thus permitting an algorithmic solution to the model checking problem.
Abstract: We consider the problem of model checking message-passing systems with real-time requirements. As behavioural specifications, we use message sequence charts (MSCs) annotated with timing constraints. Our system model is a network of communicating finite state machines with local clocks, whose global behaviour can be regarded as a timed automaton. Our goal is to verify that all timed behaviours exhibited by the system conform to the timing constraints imposed by the specification. In general, this corresponds to checking inclusion for timed languages, which is an undecidable problem even for timed regular languages. However, we show that we can translate regular collections of time-constrained MSCs into a special class of event-clock automata that can be determinized and complemented, thus permitting an algorithmic solution to the model checking problem.
14 citations
TL;DR: In this article, the authors introduce infinite time computable model theory, a model theory arising with infinite time Turing machines, which provides infinitary notions of computability for structures built on the real real number R. The analysis makes use of techniques both from computability theory and set theory.
Abstract: We introduce infinite time computable model theory, the com- putable model theory arising with infinite time Turing machines, which provide infinitary notions of computability for structures built on the reals R. Much of the finite time theory generalizes to the infinite time context, but several fundamental questions, including the infinite time computable analogue of the Completeness Theorem, turn out to be independent of zfc. Computable model theory is model theory with a view to the computability of the structures and theories that arise (for a standard reference, see (EGNR98)). Infinite time computable model theory, which we introduce here, carries out this program with the infinitary notions of computability provided by infinite time Turing ma- chines. The motivation for a broader context is that, while finite time computable model theory is necessarily limited to countable models and theories, the infinitary context naturally allows for uncountable models and theories, while retaining the computational nature of the undertaking. Many constructions generalize from finite time computable model theory, with structures built on N, to the infinitary theory, with structures built on R. In this article, we introduce the basic theory and con- sider the infinitary analogues of the completeness theorem, the Lowenheim-Skolem Theorem, Myhill's theorem and others. It turns out that, when stated in their fully general infinitary forms, several of these fundamental questions are independent of zfc. The analysis makes use of techniques both from computability theory and set theory. This article follows up (Ham05). 1.1. Infinite time Turing machines. The definitive introduction to infinite time Turing machines appears in (HL00), but let us quickly describe how they work. The
14 citations