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Monadic Second-Order Logic over Rectangular Pictures and Recognizability by Tiling Systems
1996
Information and Computation
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It is shown that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system iff it is definable in existential monadic second-order logic. ...
As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and also matches ...
monadic second-order logic is established. ...
doi:10.1006/inco.1996.0018
fatcat:wftquihpyjd5jojgjhqff3tlum
Automata theory on trees and partial orders
[chapter]
1997
Lecture Notes in Computer Science
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Graph acceptors and their specialization for pictures, \tiling systems", are presented, and their equivalence to existential monadic second-order logic is reviewed. ...
Other restricted versions of graph acceptors are discussed, and an intuitive exposition of the recently established monadic quanti er alternation hierarchy over graphs is given. ...
How large is the gap between recognizability and de nability in full monadic second-order logic? ...
doi:10.1007/bfb0030586
fatcat:xe7c4rmzbvautdrin2igsfgurq
Uniform and nonuniform recognizability
2003
Theoretical Computer Science
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, nonuniform recognizability, and monadic second-order logic. ...
We show how this approach encompasses known models of nondeterministic automata over ÿnite words, trees, pictures, and graphs, and present some elementary metaresults connecting uniform recognizability ...
expressions, and monadic second-order logic. ...
doi:10.1016/s0304-3975(01)00229-8
fatcat:4btfarn3pfdchiijplmiesg4wa
Page 7660 of Mathematical Reviews Vol. , Issue 95m
[page]
1995
Mathematical Reviews
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second-order logic over pictures and recognizability by tiling systems. ...
In fact it is proved that the family of picture languages recognised by finite tiling sys- tems coincides with the family of picture languages definable in existential monadic second-order logic. ...
Two-Dimensional Languages
[chapter]
1997
Handbook of Formal Languages
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Thomas and S. Seibert for many useful discussions on the relationship between logic and tiling systems. We are grateful to M. Latteux and D. ...
Simplot for sending us a copy of 25], and for many useful comments on domino systems, and to V. Bruyere for sending us a copy of A. Gilon's Thesis 16]. K. ...
monadic second order logic (cf. 38] ). ...
doi:10.1007/978-3-642-59126-6_4
fatcat:ymevasf56jbxfkqnos6wvzlocu
Page 6559 of Mathematical Reviews Vol. , Issue 2000i
[page]
2000
Mathematical Reviews
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[Inform. and Comput. 125 (1996), no. 1, 32-45; MR 97c:68109], regarding the expressive equivalence between existential monadic second-order logic and recognizability by tiling systems. ...
Two results are shown: the first exhibits a class of graphs where the use of “occurrence constraints” in tiling systems can be avoided, and the second shows that over pictures (i.e., over labelled rectangular ...
Weighted Picture Automata and Weighted Logics
[chapter]
2006
Lecture Notes in Computer Science
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We establish a notion of a weighted MSO logics over pictures. The semantics of a weighted formula will be a picture series. ...
We introduce weighted 2-dimensional on-line tessellation automata (W2OTA) and prove that for commutative semirings, the class of picture series defined by sentences of the weighted logics coincides with ...
The author would like to thank Manfred Droste and Dietrich Kuske for their helpful discussions and comments on earlier versions of this paper. ...
doi:10.1007/11672142_25
fatcat:bynebp2vwfdu3e365fjuld7khi
Perfectly quilted rectangular snake tilings
2009
Theoretical Computer Science
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We introduce a particular form of snake tilings to define picture languages, and relate the obtained family to the recognizable picture languages (as defined by Wang tiles). ...
The correspondence for substitution tilings is even closer, and hence is applicable to the Hilbert curve. ...
Acknowledgements We are indebted to Klaus Reinhardt and Jarkko Kari for providing helpful information. We thank the referees for suggestions that improved our presentation. ...
doi:10.1016/j.tcs.2008.12.010
fatcat:6pwzjem2yzfllpbpa24yq3z2xq
EMSO-logic and automata related to homogeneous flow event structures
2004
Theoretical Computer Science
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In this paper we study the recognizability and deÿnability on existential monadic second order (EMSO) logic of languages related to homogeneous ow event structures (HFES), i.e., the languages of conÿgurations ...
If G is the domain of linear order or binary tree then the recognizability and EMSO-deÿnability of conÿgurations of HFES hold. ...
The binary tree t is represented by the tree model t = (dom(t); S t 1 ; S t 2 ; ¡ t ; In logical formulas we use ÿrst-order variables x; y; z; : : : for positions, and monadic second-order variables X; ...
doi:10.1016/j.tcs.2004.03.030
fatcat:z7e5hjqdjnaf5dikcyzfzm6oty
Bisimulation-invariant PTIME and higher-dimensional μ-calculus
1999
Theoretical Computer Science
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Biichi-Elgot-Trakhtenbrot Theorem (the automaton-recognizable properties of finite words are those that are definable in monadic second-order logic), or the Immerman-Vardi Theorem (the PTIME properties ...
Paradigmatic results in this area are, for instance, Fagin's Theorem (the NP-recognizable properties of finite structures are exactly those that can be formalized in existential second-order logic), the ...
second-order logic. ...
doi:10.1016/s0304-3975(98)00314-4
fatcat:klwctsikb5fhpm45567db6vn6y
Characterizations of recognizable picture series
2007
Theoretical Computer Science
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the families of series characterized by weighted tiling or weighted domino systems. ...
We assign weights to different devices, ranging from picture automata to tiling systems. ...
Acknowledgements The author would like to thank Manfred Droste and Paul Gastin for their helpful discussions and comments on earlier versions of this paper, as well as the work of the unknown referees ...
doi:10.1016/j.tcs.2007.01.019
fatcat:wopdjrx7wbcefiamcdr2opra4m
Weighted Automata and Logics on Graphs
[chapter]
2015
Lecture Notes in Computer Science
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Weighted automata model quantitative features of the behavior of systems and have been investigated for various structures like words, trees, traces, pictures, and nested words. ...
As a consequence, we obtain corresponding Büchi-type equivalence results known from the recent literature for weighted automata and weighted logics on words, trees, pictures, and nested words. ...
Conclusion We introduced a weighted generalization of Thomas' graph acceptors [33, 34] and a suitable weighted logic in the sense of Droste and Gastin [9] . ...
doi:10.1007/978-3-662-48057-1_15
fatcat:d53kbssbsbhozbxyh6yhxjc6cy
On some recognizable picture-languages
[chapter]
1998
Lecture Notes in Computer Science
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We show that the language of pictures over fa; bg, where all occurring b's are connected is recognizable, which solves an open problem in Mat98]. ...
Furthermore we show that the language of pictures over fa; bg, where the number of a's is equal to the number of b's is nonuniformly recognizable. ...
A set (language) of pictures is called recognizable if it is recognized by a nite tiling system. ...
doi:10.1007/bfb0055827
fatcat:jkoijn4tdne6lkpo53pumcwqqa
Unambiguous recognizable two-dimensional languages
2006
RAIRO - Theoretical Informatics and Applications
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Some closure and non-closure properties of UREC are presented. Finally we show that it is undecidable whether a given tiling system is unambiguous. ...
Further UREC family coincides with the class of picture languages defined by unambiguous 2OTA and it strictly contains its deterministic counterpart. ...
Moreover finite tiling systems have also a natural logic meaning: in [11, 12] it is shown that the family REC and the family of languages defined by existential monadic second order formulas coincide ...
doi:10.1051/ita:2006008
fatcat:6ad3fsdvzfesbeanox4kenvwny
Weighted Automata and Logics on Infinite Graphs
[chapter]
2016
Lecture Notes in Computer Science
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This gives us the first general results connecting automata and logics over infinite graphs in the qualitative and the quantitative setting. ...
We show a Büchi-like connection between graph automata and logics for infinite graphs. ...
Acknowledgments: I want to thank Manfred Droste and Tobias Weihrauch for helpful discussions and insightful remarks on earlier drafts of this paper. ...
doi:10.1007/978-3-662-53132-7_13
fatcat:jkr7qckpq5fnnk53qf26mybqgy
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