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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16 Jul 2011
TL;DR: In this article, the complexity of reasoning for spatial constraint languages with equality, contact and connectedness predicates was investigated, and it was shown that the complexity varies dramatically depending on the dimension of the space and on the type of regions considered.
Abstract: We investigate (quantifier-free) spatial constraint languages with equality, contact and connectedness predicates, as well as Boolean operations on regions, interpreted over low-dimensional Euclidean spaces. We show that the complexity of reasoning varies dramatically depending on the dimension of the space and on the type of regions considered. For example, the logic with the interior-connectedness predicate (and without contact) is undecidable over polygons or regular closed sets in R2, EXPTIME-complete over polyhedra in R3, and NP-complete over regular closed sets in R3.
14 citations
TL;DR: It is shown that the problem whether an arbitrary regular language has a non-empty decomposable sublanguage with respect to a fixed distribution is decidable if and only if the independence relation induced by the distribution is transitive.
Abstract: It is shown that the problem whether an arbitrary regular language has a non-empty decomposable sublanguage with respect to a fixed distribution is decidable if and only if the independence relation induced by the distribution is transitive. A sufficient condition on the distributed control architecture is then derived, under which there exist some fixed non-blocking local generators such that the distributed supervisor synthesis problem is undecidable. We also show that a natural formulation of the parameterized supervisor synthesis problem is undecidable for a fixed non-blocking generator template, so long as the template alphabet has at least two private events and one global event that are controllable. In particular, all the undecidability results are still valid even if star free specification languages are considered.
14 citations
02 Mar 2015
TL;DR: This work identifies a restriction – which is called weakness – of CMA, and shows that they are equivalent to three existing forms of automata over data languages, and that in the deterministic case they are closed under all Boolean operations, and hence have an ExpSpace-complete equivalence problem.
Abstract: Automata over infinite alphabets have recently come to be studied extensively as potentially useful tools for solving problems in verification and database theory. One popular model of automata studied is the Class Memory Automata (CMA), for which the emptiness problem is equivalent to Petri Net Reachability. We identify a restriction – which we call weakness – of CMA, and show that they are equivalent to three existing forms of automata over data languages. Further, we show that in the deterministic case they are closed under all Boolean operations, and hence have an ExpSpace-complete equivalence problem. We also extend CMA to operate over multiple levels of nested data values, and show that while these have undecidable emptiness in general, adding the weakness constraint recovers decidability of emptiness, via reduction to coverability in well-structured transition systems. We also examine connections with existing automata over nested data.
14 citations
01 Jan 2009
TL;DR: Using the fact that the tiling problem of Wang tiles is undecidable even if the given tile set is deterministic by two opposite corners, it was shown in this article that the question of whether there exists a trajectory which belongs to the given open and closed set is also undecidability for one-dimensional reversible cellular automata.
Abstract: Using the fact that the tiling problem of Wang tiles is undecidable even if the given tile set is deterministic by two opposite corners, it is shown that the question whether there exists a trajectory which belongs to the given open and closed set is undecidable for one-dimensional reversible cellular automata This result holds even if the cellular automaton is mixing Furthermore, it is shown that left expansivity of a reversible cellular automaton is an undecidable property Also, the tile set construction gives yet another proof for the universality of one-dimensional reversible cellular automata
14 citations
TL;DR: It is shown that it is undecidable whether or not two finite substitutions are equivalent on the fixed regular language ab*c, which gives an unexpected answer to a question proposed in 1985 by Culik II and Karhumaki.
Abstract: We show that it is undecidable whether or not two finite substitutions are equivalent on the fixed regular language ab*c. This gives an unexpected answer to a question proposed in 1985 by Culik II and Karhumaki. At the same time it can be seen as the final result in a series of undecidability results for finite transducers initiated in 1968 by Griffiths. An application to systems of equations over finite languages is given.
14 citations