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Set constraints with projections are in NEXPTIME

W. Charatonik, L. Pacholski
Proceedings 35th Annual Symposium on Foundations of Computer Science  
In this paper we prove that the problem of existence of a solution of a system of set constraints with projections is in NEXPTIME, and thus that it is NEXPTIMEcomplete. This extends the result of A .  ...  Systems of set constraints describe relations between sets of ground terms. They have been successfully used in program analysis and type inference.  ...  In this paper we give solution to the full problem, i.e we prove that the problem of existence of a solution of set constraints with projections is NEXPTIME complete.  ... 
doi:10.1109/sfcs.1994.365727 dblp:conf/focs/CharatonikP94 fatcat:pjqh566jsbfgpo2yim3ucleyiq

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.  ...  Then formulas F and F ′ are equisatisfiable and their satisfying assignments have the same projections on the set and multiset variables occurring in F .  ... 
doi:10.1007/978-3-642-11319-2_27 fatcat:26myazvvhrgozjfoxqg73ob4aq

On the Satisfiability of Context-free String Constraints with Subword-Ordering

C. Aiswarya, Soumodev Mal, Prakash Saivasan
2022 Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science  
We consider a fragment in which the subwordorder constraints do not impose any cyclic dependency between variables. We show that this fragment is NexpTime-complete.  ...  We consider a variant of string constraints given by membership constraints in context-free languages and subword relation between variables.  ...  In fact we show that the problem is already NexpTime hard when the membership constraints are given as regular languages.  ... 
doi:10.1145/3531130.3533329 fatcat:3dud2qg52vgl5nyqqeglrybt5e

Feasible Automata for Two-Variable Logic with Successor on Data Words [chapter]

Ahmet Kara, Thomas Schwentick, Tony Tan
2012 Lecture Notes in Computer Science  
They can be characterized by the extension of EMSO 2 (+1, ∼) with existential quantifiers for infinite sets.  ...  It follows from previous work, David, et. al. in 2010 , that the nonemptiness problem for weak data automata can be decided in 2-NEXPTIME. Furthermore, we study weak Büchi automata on data ω-strings.  ...  A more direct proof with a 4-NEXPTIME bound was given in [9] and a 2-NEXPTIME bound was obtained in [20] .  ... 
doi:10.1007/978-3-642-28332-1_30 fatcat:5pods2csn5e7zdr53mgtekqv6m

Order-Invariance of Two-Variable Logic is Decidable [article]

Thomas Zeume, Frederik Harwath
2016 arXiv   pre-print
In addition, the finite satisfiability problem for ESO^2 on structures with one linear order and its induced successor relation is shown to be decidable in non-deterministic exponential time.  ...  We also show that finite satisfiability is decidable on structures with two successors and one induced linear order. In both cases, so far only decidability for monadic ESO^2 has been known.  ...  NExpTime-complete [7] NExpTime-complete Two linear orders/successors (S 1 , S 2 )-structures NExpTime-complete [3] NExpTime-complete [3] (< 1 , < 2 )-structures in ExpSpace [24] in 2-NExpTime  ... 
arXiv:1604.05843v1 fatcat:t7hsd7ja5zhjlgmwi235epm3tm

Two-variable logic and key constraints on data words

Matthias Niewerth, Thomas Schwentick
2011 Proceedings of the 14th International Conference on Database Theory - ICDT '11  
As a byproduct, a selfcontained exposition of an algorithm that decides satisfiability of such formulas (without key constraints) in 2-nexptime is given.  ...  The paper introduces key constraints for data words and shows that it is decidable whether, for a given two-variable sentence ϕ that can refer to the successor relation on positions and a set K of key  ...  More precisely, A5 has to test that only one position in the string projection is matched by κ. Let K5 be the set of key constraints that are obtained in this way.  ... 
doi:10.1145/1938551.1938571 dblp:conf/icdt/NiewerthS11 fatcat:nge44rsfvjb3tgrphosgncoyfe

Satisfiability for two-variable logic with two successor relations on finite linear orders [article]

Diego Figueira
2013 arXiv   pre-print
We show that the problem is decidable in NEXPTIME.  ...  We study the finitary satisfiability problem for first order logic with two variables and two binary relations, corresponding to the induced successor relations of two finite linear orders.  ...  Suppose there are exactly k ≤ k columns that are not among {c 1 , . . . , c k } with k constraints.  ... 
arXiv:1204.2495v3 fatcat:hvc3msmleff4dbcmthkvfhttnq

Reasoning About Actions Using Description Logics with General TBoxes [chapter]

Hongkai Liu, Carsten Lutz, Maja Miličić, Frank Wolter
2006 Lecture Notes in Computer Science  
However, existing DL action formalisms fail to include general TBoxes, which are the standard tool for formalising ontologies in modern description logics.  ...  and computational complexity of reasoning in our formalism.  ...  The first author was supported by the DFG Project BA1122/10-2. The second author was supported by the EU funded IST-2005-7603 FET Project Thinking Ontologies (TONES).  ... 
doi:10.1007/11853886_23 fatcat:25bxiylhjzhhnm3j6dsx5obobe

Extending Büchi Automata with Constraints on Data Values [article]

Ahmet Kara, Tony Tan
2012 arXiv   pre-print
These are trees or words that, in addition to labels from a finite alphabet, carry data values from an infinite alphabet (data).  ...  In general it is rather hard to obtain logics for data words and trees that are sufficiently expressive, but still have reasonable complexity for the satisfiability problem.  ...  with label b; while denial-constraint states that the sets of data values found in positions with labels a and b are disjoint.  ... 
arXiv:1012.5439v2 fatcat:wzw65wkzlnfqhfduuendca5a2u

DL Actions with GCIs: a Pragmatic Approach

Hongkai Liu, Carsten Lutz, Maja Milicic, Frank Wolter
2006 International Workshop on Description Logics  
In this paper, we define DL action formalisms that admit GCIs, propose a pragmatic approach to addressing the ramification problem that is introduced in this way, show that our formalim is decidable and  ...  Projection and executability are co-NExpTime-complete, while weak consistency is NExpTime-complete in ALCQIO and ALCQI.  ...  Projection and executability (weak consistency) in ALCQI are co-NExpTime-hard ( NExpTime-hard) even if occlusions for roles are restricted to {(⊥, ⊥)} and only nominals are allowed in the occlusions of  ... 
dblp:conf/dlog/LiuLMW06 fatcat:qhf7nuk66jad7m3hu6dirlva3a

Atomic Set Constraints with Projection [chapter]

Witold Charatonik, Jean-Marc Talbot
2002 Lecture Notes in Computer Science  
This class subsumes some already studied classes such as atomic set constraints with left-hand side projection and INES constraints.  ...  In the case of atomic set constraints with projection one might expect that satisfiability remains polynomial.  ...  We show that it works in PSPACE, while the only previously known algorithm covering this class of constraints (devised for the general set constraints with projections [7] ) worked in NEXPTIME.  ... 
doi:10.1007/3-540-45610-4_22 fatcat:snstgyv7bvgtbjjc3pvqnnfdv4

On Quantified Propositional Logics and the Exponential Time Hierarchy

Miika Hannula, Juha Kontinen, Martin Lück, Jonni Virtema
2016 Electronic Proceedings in Theoretical Computer Science  
We show that DQBF formulae correspond naturally to quantified propositional dependence logic and present a general NEXPTIME upper bound for quantified propositional logic with a large class of generalized  ...  Moreover we show AEXPTIME(poly)-completeness for extensions of propositional team logic with generalized dependence atoms.  ...  Miika Hannula was supported by the FRDF grant of the University of Auckland (project 3706751). Juha Kontinen and Jonni Virtema were supported by grant 292767 of the Academy of Finland.  ... 
doi:10.4204/eptcs.226.14 fatcat:ab3al4k7mvdfdab6fnfgvbvsuu

Set constraints: Results, applications and future directions [chapter]

Alexander Aiken
1994 Lecture Notes in Computer Science  
Set constraints are a natural formalism for many problems that arise in program analysis.  ...  This paper provides a brief introduction to set constraints: what set constraints are, why they are interesting, the current state of the art, open problems, applications and implementations.  ...  constraints with projections CP94b].  ... 
doi:10.1007/3-540-58601-6_110 fatcat:3ccf5wz6wvfs7hvgrtxx6xjh64

Commutative Data Automata

Zhilin Wu, Marc Herbstritt
2012 Annual Conference for Computer Science Logic  
In weak data automata, the class conditions are specified by some simple constraints on the number of occurrences of labels occurring in every class.  ...  , more precisely, in 3-NEXPTIME.  ...  The nonemptiness of weak data automata can be decided with elementary complexity, more precisely, in 2-NEXPTIME.  ... 
doi:10.4230/lipics.csl.2012.528 dblp:conf/csl/Wu12 fatcat:djq7jkebtvbdvoe56ht3xkchkm

A NExpTime-Complete Description Logic Strictly Contained in C 2 [chapter]

Stephan Tobies
1999 Lecture Notes in Computer Science  
This combination can naturally be embedded into C 2 , the two variable fragment of predicate logic with counting quanti ers.  ...  We examine the complexity and expressivity of the combination of the Description Logic ALCQI with a terminological formalism based on cardinality restrictions on concepts.  ...  A domino system is a triple D = (D; H; V ), where D is a nite set (of tiles) and H; V D D are relations expressing horizontal and vertical compatibility constraints between the tiles.  ... 
doi:10.1007/3-540-48168-0_21 fatcat:a7f7ky3anzhkxi34zeqemtbq44
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