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The Domino Problem for Self-similar Structures
[chapter]
2016
Lecture Notes in Computer Science
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In this setting we exhibit non-trivial families of subsets with decidable and undecidable domino problem. ...
We define the domino problem for tilings over self-similar structures of Z d given by forbidden patterns. ...
Connectivity Isthmus Weak grid Strong grid DP decidable Unknown DP undecidable DP undecidable
Concluding remarks In this article we introduced a version of the domino problem on self-similar structures ...
doi:10.1007/978-3-319-40189-8_21
fatcat:uuiessd3tbca7ekqjroygyzana
On the solvability of domino snake problems
1994
Theoretical Computer Science
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Myers, On the solvability of domino snake problems, Theoretical Computer Science 131 (1994) 243-269. ...
In this paper we present an extensive treatment of tile connecrability problems, sometimes called domino snake problems. ...
Less known is the family of tile connectability problems, or domino snake problems. ...
doi:10.1016/0304-3975(94)90174-0
fatcat:mrdbkye4zfdexgty4psngbojye
The domino problem on groups of polynomial growth
[article]
2018
arXiv
pre-print
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We characterize the virtually nilpotent finitely generated groups (or, equivalently by Gromov's theorem, groups of polynomial growth) for which the Domino Problem is decidable: These are the virtually ...
free groups, i.e. finite groups, and those having as a subgroup of finite index. ...
DECIDABILITY OF THE DOMINO PROBLEM In this section we reduce the undecidability of the domino problem in groups with the 'half-grid' structure found in Section 3 to the undecidability of the domino problem ...
arXiv:1311.4222v4
fatcat:af5ubc5vuzbz5iqmfchgts4d7m
Monadic second-order logic and the domino problem on self-similar graphs
[article]
2020
arXiv
pre-print
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On the other hand, we already prove undecidability of the domino problem for a class of self-similar groups, answering a question by Barbieri and Sablik, and some examples including one of linear growth ...
We consider the domino problem on Schreier graphs of self-similar groups, and more generally their monadic second-order logic. ...
Undecidability results We now prove that the domino problem is undecidable on some examples of self-similar graphs. ...
arXiv:2011.02735v1
fatcat:vun3sghucve7zglgusdaq65a54
Undecidability of PDL with L = {a2i |; i ⩾ 0}
1984
Journal of computer and system sciences (Print)
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It is shown that the validity problem for propositional dynamic logic (PDL), which is decidable and actually DEXPTIME-complete for the usual class of regular programs, becomes highly undecidable, viz. ...
This answers a question of Harel, Pnueli, and Stavi. 0 1984 Academic Press, Inc. ...
UNDECIDABILITY OF PDL WITH I!, = (u" 1 i > o} ...
doi:10.1016/0022-0000(84)90005-9
fatcat:f7udt723qvapddi7nllcfp4npe
The Domino Problem is Undecidable on Surface Groups
2019
International Symposium on Mathematical Foundations of Computer Science
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As an application, we prove that the domino problem is undecidable for the fundamental group of any closed orientable surface of genus at least 2. ...
We show that the domino problem is undecidable on orbit graphs of non-deterministic substitutions which satisfy a technical property. ...
An important property of the domino problem is that groups which contain subgroups with undecidable domino problem have themselves undecidable domino problem [6, Proposition 9.3.30] . ...
doi:10.4230/lipics.mfcs.2019.46
dblp:conf/mfcs/AubrunBM19
fatcat:pzzwocsetnbv7pqnuo3ir2344e
The domino problem on groups of polynomial growth
2018
Groups, Geometry, and Dynamics
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Our proof uses a reduction of the undecidability of the domino problem on groups with infinite tree-width to the undecidability of the domino problem on Z 2 . ...
We characterize the virtually nilpotent finitely generated groups (or, equivalently by Gromov's theorem, groups of polynomial growth) for which the Domino Problem is decidable: These are the virtually ...
This means that v i w i 1 . . . w i ki = v i ′ w i ′ 1 . . . w i k i ′ for some i ̸ = i ′ ,
DECIDABILITY OF THE DOMINO PROBLEM In this section we reduce the undecidability of the domino problem in ...
doi:10.4171/ggd/439
fatcat:3yrldil3bveutoxjtsgquoa7fe
Translation-like Actions and Aperiodic Subshifts on Groups
[article]
2015
arXiv
pre-print
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weakly aperiodic SFT (and actually a undecidable domino problem). ...
It is well known that if G admits a f.g. subgroup H with a weaklyaperiodic SFT (resp. an undecidable domino problem), then Gitself has a weakly aperiodic SFT (resp. an undecidable domino problem).We prove ...
has undecidable domino problem. ...
arXiv:1508.06419v1
fatcat:dnrdibpfuvbkfgcml2e7kfoaee
Undecidability of the transitive graded modal logic with converse
2016
Journal of Logic and Computation
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The method of proof deserves a few words. We prove the undecidability by reduction from the undecidable domino problem for Z×Z. ...
As a consequence, for the "unrestricted version" of the description logic SIQ, the problem of concept satisfiability (even with respect to the empty terminology) is undecidable. ...
Domino problem Our undecidability proofs are given by reduction from the undecidable "domino problem". ...
doi:10.1093/logcom/exw026
fatcat:kqxfawxah5f5djgsv2dnugwseu
Satisfiability vs. Finite Satisfiability in Elementary Modal Logics
2012
Electronic Proceedings in Theoretical Computer Science
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finite satisfiability problem, but undecidable general satisfiability problem. ...
with decidable (global) satisfiability problem, but undecidable finite satisfiability problem, and, the other way round, that there is a universal formula that defines an elementary modal logic with decidable ...
Is there a universal first-order formula Φ such that the global satisfiability problem of modal logic over K Φ is NEXPTIME-hard and decidable? ...
doi:10.4204/eptcs.96.11
fatcat:mo6aflstjndjtn6qkikytufo7e
Consistency of multidimensional combinatorial substitutions
2012
Theoretical Computer Science
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We prove that it is undecidable whether a two-dimensional substitution is consistent or overlapping, and we provide practical algorithms to decide these properties in some particular cases. ...
Two problems can arise when defining a substitution in such a way: it can fail to be consistent, and the patterns in an image by the substitution might overlap. ...
This research is supported by the Academy of Finland Grant 131558. ...
doi:10.1016/j.tcs.2012.03.050
fatcat:qsa7zlfv3fgs3du6vt6b3zheui
Consistency of Multidimensional Combinatorial Substitutions
[chapter]
2012
Lecture Notes in Computer Science
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We prove that it is undecidable whether a two-dimensional substitution is consistent or overlapping, and we provide practical algorithms to decide these properties in some particular cases. ...
Two problems can arise when defining a substitution in such a way: it can fail to be consistent, and the patterns in an image by the substitution might overlap. ...
This research is supported by the Academy of Finland Grant 131558. ...
doi:10.1007/978-3-642-30642-6_20
fatcat:b2rwzp7b4neznoi6fbbafu345a
The domino problem is undecidable on surface groups
[article]
2018
arXiv
pre-print
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As an application, we prove that the domino problem is undecidable for the fundamental group of any closed orientable surface of genus at least 2. ...
We show that the domino problem is undecidable on orbit graphs of non-deterministic substitutions which satisfy a technical property. ...
We would also grateful to Yann Ollivier for his pictures of the Cayley graph of the surface group [16] , the one in the front page being one of them. ...
arXiv:1811.08420v1
fatcat:qjkw6u2pz5hulb4lyuozx2o4ly
Preface
2009
Theoretical Computer Science
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The domino problem is the decision problem for determining whether a given set of Wang tiles admits a tiling of the infinite plane. Proved undecidable by R. ...
Berger in the 60's, the domino problem has become an important tool for establishing undecidability results in various systems, including cellular automata. The paper by V. ...
Jarkko Kari Department of Mathematics, University of Turku, FI-20014, Finland ...
doi:10.1016/j.tcs.2008.12.002
fatcat:ghm2oc3k35hrzncrp7flzothhq
Consensus Game Acceptors
[chapter]
2015
Lecture Notes in Computer Science
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The players have a joint objective to avoid an inadmissible decision, in spite of the uncertainty induced by the input. ...
Uniform encoding of domino problems in games Game formulations of domino tiling problems are standard in complexity theory, going back to the early work of Chlebus [7] . ...
As the emptiness problem for contextsensitive languages is undecidable [12] , it follows that the solvability problem is undecidable for consensus game acceptors. ...
doi:10.1007/978-3-319-21500-6_8
fatcat:6jzwrwgegbdi5a7rblyf7buhbe
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