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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TL;DR: It is shown that for other two-dimensional systems, the reachability question remains unanswered, by proving that it is as hard as the reachable problem for piecewise affine maps on the real line, which is a well known open problem.
Abstract: Even though many attempts have been made to define the boundary between decidable and undecidable hybrid systems, the affair is far from being resolved. More and more low dimensional systems are being shown to be undecidable with respect to reachability, and many open problems in between are being discovered. In this paper, we present various two-dimensional hybrid systems for which the reachability problem is undecidable. We show their undecidability by simulating Minsky machines. Their proximity to the decidability frontier is understood by inspecting the most parsimonious constraints necessary to make reachability over these automata decidable. We also show that for other two-dimensional systems, the reachability question remains unanswered, by proving that it is as hard as the reachability problem for piecewise affine maps on the real line, which is a well known open problem.
32 citations
04 May 2015
TL;DR: This work proposes a variant of arbitrary public announcement logic which is decidable and provides a proof-of-concept to show its expressiveness, and uses this framework to reason about epistemic properties and arbitrary announcements when agents are cameras located in the plane.
Abstract: We propose a variant of arbitrary public announcement logic which is decidable. In this variant, knowledge accessibility relations are defined by programs. Technically, programs are written in dynamic logic with propositional assignments. We prove that both the model checking problem and the satisfiability problem are decidable and AEXPpol-complete where AEXPpol is the class of decision problems decided by alternating Turing machines running in exponential time where the number of alternations is polynomial. Whereas arbitrary public announcement logic is undecidable, our framework is decidable and we provide a proof-of-concept to show its expressiveness: we use our framework to reason about epistemic properties and arbitrary announcements when agents are cameras located in the plane.
32 citations
24 Mar 2012
TL;DR: This work considers the model-checking problem for data multi-pushdown automata (DMPA), and states that one can decide if all words generated by a DMPA satisfy a given formula from the full MSO logic.
Abstract: We consider the model-checking problem for data multi-pushdown automata (DMPA). DMPA generate data words, i.e, strings enriched with values from an infinite domain. The latter can be used to represent an unbounded number of process identifiers so that DMPA are suitable to model concurrent programs with dynamic process creation. To specify properties of data words, we use monadic second-order (MSO) logic, which comes with a predicate to test two word positions for data equality. While satisfiability for MSO logic is undecidable (even for weaker fragments such as first-order logic), our main result states that one can decide if all words generated by a DMPA satisfy a given formula from the full MSO logic.
32 citations
TL;DR: A new undecidability result about tiling problems is given, given a finite set of polyomino types, the problem whether this set is a code, is undecidable.
32 citations
TL;DR: The inclusion problem for pattern languages is studied to demonstrate that there is no effective procedure deciding the inclusion for the class of all pattern languages over all alphabets, and to disproves the prevalent conjecture on the inclusion of so-called similar E-pattern languages.
Abstract: We study the inclusion problem for pattern languages, which-due to Jiang et al. [T. Jiang, A. Salomaa, K. Salomaa, S. Yu, Decision problems for patterns, Journal of Computer and System Sciences 50 (1995) 53-63]-is known to be undecidable. More precisely, Jiang et al. demonstrate that there is no effective procedure deciding the inclusion for the class of all pattern languages over all alphabets. Most applications of pattern languages, however, consider classes over fixed alphabets, and therefore it is practically more relevant to ask for the existence of alphabet-specific decision procedures. Our first main result states that, for all but very particular cases, this version of the inclusion problem is also undecidable. The second main part of our paper disproves the prevalent conjecture on the inclusion of so-called similar E-pattern languages, and it explains the devastating consequences of this result for the intensive previous research on the most prominent open decision problem for pattern languages, namely the equivalence problem for general E-pattern languages.
32 citations