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Tarskian set constraints are in NEXPTIME [chapter]

Pawel Mielniczuk, Leszek Pacholski
1998 Lecture Notes in Computer Science  
In this paper we show that satis ability of Tarskian set constraints (without recursion) can be decided in exponential time. This closes the gap left open by D.A. McAllester, R. Givan, C.  ...  Kozen in 14].  ...  Here we give a NEXPTIME algorithm solving full systems of Tarskian set constraints (without recursion). We do it without a reduction to systems of prequadratic Diophantine inequalities.  ... 
doi:10.1007/bfb0055809 fatcat:l4sdfaz55jfbvfswnt5nl7sozi

Tarskian Set Constraints

Robert Givan, David McAllester, Carl Witty, Dexter Kozen
2002 Information and Computation  
We show that satisfiability of Tarskian set constraints is decidable in nondeterministic doubly exponential time.  ...  Unlike the Herbrand constructor symbols used in recent set constraint formalisms, the meaning of a Tarskian function symbol is interpreted in an arbitrary first order structure.  ...  constraint sets is NEXPTIME hard.  ... 
doi:10.1006/inco.2001.2973 fatcat:s43es4umifb6tfcf45gvehaw6y

Collections, Cardinalities, and Relations [chapter]

Kuat Yessenov, Ruzica Piskac, Viktor Kuncak
2010 Lecture Notes in Computer Science  
Logics that involve collections (sets, multisets), and cardinality constraints are useful for reasoning about unbounded data structures and concurrent processes.  ...  To make such logics more useful in verification this paper extends them with the ability to compute direct and inverse relation and function images.  ...  In [10] , NEXPTIME lower bound for Tarskian set constraints with constants and binary functions is shown by reduction of a fragment of first order logic. We adapt this proof to QFBAPA-Rel.  ... 
doi:10.1007/978-3-642-11319-2_27 fatcat:26myazvvhrgozjfoxqg73ob4aq

Inclusion constraints over non-empty sets of trees [chapter]

Martin Müller, Joachim Niehren, Andreas Podelski
1997 Lecture Notes in Computer Science  
The existing systems of set constraints can express INES constraints only if they include negation. Their satisfiability problem is NEXPTIME-complete.  ...  We present a new constraint system called INES.  ...  The research reported in this paper has been supported by the the Esprit Working Group CCL II (EP 22457) and the Deutsche Forschungsgemeinschaft through the Graduiertenkolleg Kognitionswissenschaft and  ... 
doi:10.1007/bfb0030609 fatcat:4yz27c5jozhzppmavsu264nqvy

NP Decision Procedure for Monomial and Linear Integer Constraints [article]

Rodrigo Raya, Jad Hamza, Viktor Kunčak
2022 arXiv   pre-print
We show that the satisfiability of these constraints is in NP.  ...  The constraints we consider are a conjunction of a linear system Ax = b and a conjunction of non-convex constraints of the form x_i ≤ x_j^n.  ...  The NEXPTIME Bound for x i ≤ x j x k Constraints In this section, we review the proof of NEXPTIME complexity for general prequadratic constraints.  ... 
arXiv:2208.02713v1 fatcat:tepkxyqmmzapdma7muxvylxuji

Page 8755 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
of one-tape off-line TMs (580-588); Pawel Mielniczuk and Leszek Pacholski, Tarskian set constraints are in NEXPTIME (589-596); Sergei Vorobyov [S.  ...  8755 diagonalization strength of resource-bounded random sets (465— 473); Levke Bentzien, Positive Turing and truth-table complete- ness for NEXP are incomparable (474-482); Judy Goldsmith, Mitsunori Ogihara  ... 

Resolution-based decision procedures for the universal theory of some classes of distributive lattices with operators

Viorica Sofronie-Stokkermans
2003 Journal of symbolic computation  
In particular, we obtain exponential space and time decision procedures for the universal clause theory of (i) the class of all bounded distributive lattices with operators satisfying a set of (generalized  ...  This justifies a method for structure-preserving translation to clause form of universal sentences in such classes of algebras.  ...  In particular, I thank Harald Ganzinger for drawing my attention to the link with existing results on Tarskian set constraints. I also thank the referees for their helpful comments.  ... 
doi:10.1016/s0747-7171(03)00069-5 fatcat:az5ueveqwbaj3c2db7v4evjfpy

Tarskian set constraints

D.A. McAllester, R. Givan, C. Witty, D. Kozen
Proceedings 11th Annual IEEE Symposium on Logic in Computer Science  
We show that satisfiability of Tarskian set constraints is decidable in nondeterministic doubly exponential time.  ...  Unlike the Herbrand constructor symbols used in recent set constraint formalisms, the meaning of a Tarskian function symbol is interpreted in an arbitrary first order structure.  ...  constraint sets is NEXPTIME hard.  ... 
doi:10.1109/lics.1996.561313 dblp:conf/lics/McAllesterGWK96 fatcat:egiwztqaqffflej7xan2kc3nmy

Logical queries over views

James Bailey, Guozhu Dong, Anthony WIDJAJA To
2010 ACM Transactions on Computational Logic  
Views currently occupy a central place in database research due to their role in applications such as information integration and data warehousing.  ...  A first-order view query is a first-order formula expressed solely in terms of the given views.  ...  Theorem 4.1 implies we can test whether Q 1 (x) ⊆ Q 2 (x) under the constraints C 1 ∧ C 2 . . . ∧ C n where Q 1 , Q 2 , C 1 , . . . , C n are all first-order unary conjunctive view queries in 2-NEXPTIME  ... 
doi:10.1145/1656242.1656243 fatcat:vv2spm7q6fgmdegb7kdbwwn3ve

Logical Queries over Views: Decidability and Expressiveness [article]

James Bailey and Guozhu Dong and Anthony Widjaja To
2008 arXiv   pre-print
Views currently occupy a central place in database research, due to their role in applications such as information integration and data warehousing.  ...  Besides its theoretical interest, our new decidable class is potentially interesting for use in applications such as deciding implication of complex dependencies, analysis of a restricted class of active  ...  Theorem 4.1 implies we can test whether Q 1 (x) ⊆ Q 2 (x) under the constraints C 1 ∧ C 2 . . . ∧ C n where Q 1 , Q 2 , C 1 , . . . , C n are all first order unary conjunctive view queries in 2-NEXPTIME  ... 
arXiv:0803.2559v1 fatcat:3sulpsluj5cuvmopyuqdh3ydpi

On the Universal Theory of Varieties of Distributive Lattices with Operators: Some Decidability and Complexity Results [chapter]

Viorica Sofronie-Stokkermans
1999 Lecture Notes in Computer Science  
In this paper we establish a link between satisfiability of universal sentences with respect to varieties of distributive lattices with operators and satisfiability with respect to certain classes of relational  ...  We use these results for giving a method for translation to clause form of universal sentences in such varieties, and then use results from automated theorem proving to obtain decidability and complexity  ...  In particular, I thank Harald Ganzinger for drawing my attention to the link with existing results on Tarskian set constraints. I also thank the referees for their helpful comments.  ... 
doi:10.1007/3-540-48660-7_11 fatcat:nibtts33aja3zcvxbjtbjb5mk4

On Algorithms and Complexity for Sets with Cardinality Constraints [article]

Bruno Marnette, Viktor Kuncak, Martin Rinard
2005 arXiv   pre-print
In a quest for more efficient fragments, we identify several subclasses of sets with cardinality constraints whose satisfiability is NP-hard.  ...  Abstract sets with cardinality constraints naturally generalize typestate properties: relationships between the typestates of objects can be expressed as subset and disjointness relations on sets, and  ...  Set constraints [1, 3, 2, 6] are incomparable to the constraints studied in our paper.  ... 
arXiv:cs/0508123v1 fatcat:3log6zf4xjgbhpu4ixp65qhn7i

A Double Team Semantics for Generalized Quantifiers

Antti Kuusisto
2015 Journal of Logic, Language and Information  
We establish that the satisfiability and finite satisfiability problems of DC 2 are complete for NEXPTIME. *  ...  There are of course several ways of adding constraints that make the experiment impossible.  ...  In fact, we show that both the finite and standard satisfiability problems of DC 2 are NEXPTIME-complete.  ... 
doi:10.1007/s10849-015-9217-4 pmid:26435580 pmcid:PMC4587362 fatcat:f3qm65ypojdrviknddnvutismu

A Double Team Semantics for Generalized Quantifiers [article]

Antti Kuusisto
2017 arXiv   pre-print
Such atoms can be used in order to define extensions of first-order logic with a team-based semantics. We also define a game semantics and compare it with the double team semantics.  ...  There are of course several ways of adding constraints that make the experiment impossible.  ...  In fact, we show that both the finite and standard satisfiability problems of DC 2 are NEXPTIME-complete.  ... 
arXiv:1310.3032v19 fatcat:afltdfi7dzh4pj5jrou4djcy5u

Quantitative Logic Reasoning [article]

Marcelo Finger
2019 arXiv   pre-print
Analogous properties hold throughout that class, for whose members there exists a set of linear algebraic techniques applicable in the study of satisfiability decision problems.  ...  In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference.  ...  of a normalized set of constraints.  ... 
arXiv:1905.05665v1 fatcat:rpf6mraqavenvm7l35kabyee3q
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