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The Closure of Monadic NP

Miklos Ajtai, Ronald Fagin, Larry Stockmeyer
2000 Journal of computer and system sciences (Print)  
This paper was motivated by the desire to develop new game-theoretic tools that will enable us to prove lower bounds involving extensions of monadic NP.  ...  Our lower-bound proofs require a number of new game-theoretic techniques. 1 In an earlier version of this paper, we referred to the positive rst-order closure of monadic NP as \the 1 that are expressible  ...  the power of closed monadic NP.  ... 
doi:10.1006/jcss.1999.1691 fatcat:jiqqrl3u6zcgpo75ja7eubpleu

Easier ways to win logical games [chapter]

Ronald Fagin
1997 Descriptive Complexity and Finite Models  
This paper surveys various game-theoretic techniques and tools that lead to simpler proofs of inexpressibility results. The focus is on first-order logic and monadic NP.  ...  The key tool in proving inexpressibility results in finite-model theory is Ehrenfeucht-F'rai'ss6 games.  ...  Acknowledgements The author is grateful to Lauri Hella, Neil Immerman, Phokion Kolaitis, Clemens Lautemann, Thomas Schwentick, Larry Stockrneyer, Moshe Vardi, and Victor Vianu for helpful comments and  ... 
doi:10.1090/dimacs/031/01 dblp:conf/dimacs/Fagin96 fatcat:euzcpz5fobcuzfburbf73r43zq

Page 4134 of Mathematical Reviews Vol. , Issue 92h [page]

1992 Mathematical Reviews  
(PL-GDAN) Hierarchies of weak automata and weak monadic formulas. Theoret. Comput. Sci. 83 (1991), no. 2, Algorithms Automat. Complexity Games, 323-335.  ...  This nice result may be viewed in the general context of the theory of automata and compared to other characterizations of that kind (such as the characterization of the dot-depth hierarchy of star-free  ... 

Page 1303 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
In this article the four structures IG|;, |Gl2, Jund(G)|; and jund(G)|2, associated with a directed graph G, are compared with respect to the expressive power of monadic second-order logic, i.e. more precisely  ...  The paper is part of the author’s study of the graph properties expressible in monadic second-order logic—denoted by MS logic.  ... 

Subclasses of binary NP

A Durand
1998 Journal of Logic and Computation  
We look at semantical restrictions of binary NP, where the second order quanti ers range only over certain classes of relations.  ...  We show that many of these restrictions have the same expressive power and establish a 4-level strict hierarchy, represented by sets, permutations, unary functions and arbitrary binary relations, respectively  ...  He then used an Ehrenfeucht game to prove that the set of connected graphs (which is in monadic coNP) is not in monadic NP thus showing that monadic NP is not closed under complements Fag75].  ... 
doi:10.1093/logcom/8.2.189 fatcat:wxj3fp53brbynmvumjxw5gu7fu

Comparing the Succinctness of Monadic Query Languages over Finite Trees [chapter]

Martin Grohe, Nicole Schweikardt
2003 Lecture Notes in Computer Science  
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees.  ...  All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others.  ...  In particular, the expressive power of fragments of monadic second-order logic and various fixed-point logics has already been investigated in some of the earliest papers in finite model theory [Fag75  ... 
doi:10.1007/978-3-540-45220-1_20 fatcat:psdjunqwiffs7j4u7jjhuvkdcq

Comparing the succinctness of monadic query languages over finite trees

Martin Grohe, Nicole Schweikardt
2004 RAIRO - Theoretical Informatics and Applications  
We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees.  ...  All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others.  ...  In particular, the expressive power of fragments of monadic second-order logic and various fixed-point logics has already been investigated in some of the earliest papers in finite model theory [Fag75  ... 
doi:10.1051/ita:2004017 fatcat:s4nxmdzsorbfxoy5w4o657oqxi

On the Expressive Power of Graph Logic [chapter]

Jerzy Marcinkowski
2006 Lecture Notes in Computer Science  
In the paper [DGG04] the expressiveness power of Graph Logic is examined, and it is shown, for many MSO properties, how to express them in Graph Logic.  ...  Graph Logic, a query language being a sublogic of Monadic Second Order Logic is studied in [CGG02].  ...  In [DGG04] the expressive power of this logic is studied.  ... 
doi:10.1007/11874683_32 fatcat:mkwifpzocrg3pkhspvziakaanq

Report on BCTCS & AlgoUK 2020

Ulrich Berger, Faron Moller
2020 Bulletin of the European Association for Theoretical Computer Science  
With the scene set by the opening invited lecture by Simon Chadwick from Siemens Rail Automation UK, three of Europe's leading railway verification groups presented the state-of-the-art in railway verification  ...  diversity games; and Dr MS Ramanujan (Warwick) spoke on lossy kernelization.  ...  We study the problem of finding a stable partition, for several game-theoretic notions of stability; while some of the problems we consider turn out to be polynomial-time solvable, others are NP-hard,  ... 
dblp:journals/eatcs/BergerM20 fatcat:tnr3ji4yazgethl4qyhxkk6esm

Partially Ordered Connectives and ∑1 1 on Finite Models [chapter]

Merlijn Sevenster, Tero Tulenheimo
2006 Lecture Notes in Computer Science  
We show that Σ 1 1 ♥ harbors a strict hierarchy induced by the arity of predicate variables and that it is not closed under complementation, by means of a game-theoretical argument.  ...  : if NP = coNP then P = NP.  ...  In Section 5 we see that the slightest extension in this respects results in a logic that enjoys the expressive power of full NP.  ... 
doi:10.1007/11780342_52 fatcat:3gtphs6kbjanbid4aamemxto6y

Yuri, Logic, and Computer Science [chapter]

Andreas Blass, Nachum Dershowitz, Wolfgang Reisig
2010 Lecture Notes in Computer Science  
We illustrate two powerful decidability techniques here. One makes use of automata and games. The other is an offshoot of a composition theory where one composes models as well as their theories.  ...  J of Computer and System Sciences 49:3 (December 1994), 562-588 (Extended abstract in FOCS'89, 142-147) 85. Yuri Gurevich: The Challenger-Solver game: Variations on the Theme of P=?NP.  ... 
doi:10.1007/978-3-642-15025-8_1 fatcat:ehjpkiqxzbh55k7waxqwzfhw6y

Local Normal Forms for First-Order Logic with Applications to Games and Automata

Thomas Schwentick, Klaus Barthelmann
1999 Discrete Mathematics & Theoretical Computer Science  
\par From this and related normal forms, variants of the Ehrenfeucht game for first-order and existential monadic second-order logic are developed that restrict the possible strategies for the spoiler,  ...  \par As another application, automata models are defined that have, on arbitrary classes of relational structures, exactly the expressive power of first-order logic and existential monadic second-order  ...  Thanks also to the anonymous referees.  ... 
doi:10.46298/dmtcs.254 fatcat:y2bpqtaddnaa7lh5yc54pfnhle

Local normal forms for first-order logic with applications to games and automata [chapter]

Thomas Schwentick, Klaus Barthelmann
1998 Lecture Notes in Computer Science  
From this and related normal forms, variants of the Ehrenfeucht game for first-order and existential monadic second-order logic are developed that restrict the possible strategies for the spoiler, one  ...  As another application, automata models are defined that have, on arbitrary classes of relational structures, exactly the expressive power of first-order logic and existential monadic second-order logic  ...  Thanks also to the anonymous referees.  ... 
doi:10.1007/bfb0028580 fatcat:xcpg4m7c4ndnrp62jdbkepbmpm

A Gentle Introduction to Applications of Algorithmic Metatheorems for Space and Circuit Classes

Till Tantau
2016 Algorithms  
To this purpose, the next section first explains the basic ingredients of Courcelle's Theorem: 115 What, exactly, is monadic second-order logic and how can the concept of being "tree-like" be 116 formalized  ...  As an example, by Courcelle's Theorem, all monadic second-order ("in a certain logic") properties of graphs of bounded tree width ("structured in a certain way") can be solved in linear time ("with a certain  ...  The great power of the class NP comes from the ability of nondeterministic Turing machines to "guess" not only a single vertex, but rather a whole set of vertices.  ... 
doi:10.3390/a9030044 fatcat:4njcekeavbeufbltvu5y4rxkxa

The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory

Tomás Feder, Moshe Y. Vardi
1998 SIAM journal on computing (Print)  
This paper starts with the project of finding a large subclass of NP which exhibits a dichotomy. The approach is to find this subclass via syntactic prescriptions.  ...  While, the paper does not achieve this goal, it does isolate a class (of problems specified by) "Monotone Monadic SNP without inequality" which may exhibit this dichotomy.  ...  Milena Mihail suggested that quasirandom graphs may derandomize the representation of monotone monadic SNP in CSP.  ... 
doi:10.1137/s0097539794266766 fatcat:37znhdmmlvcdbfh3v4owh22baq
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