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Set constraints with projections are in NEXPTIME

*
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. ...

##
###
Collections, Cardinalities, and Relations
[chapter]

2010
*
Lecture Notes in Computer Science
*

Logics that involve collections (

doi:10.1007/978-3-642-11319-2_27
fatcat:26myazvvhrgozjfoxqg73ob4aq
*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 . ...##
###
On the Satisfiability of Context-free String Constraints with Subword-Ordering

2022
*
Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science
*

We consider a fragment

doi:10.1145/3531130.3533329
fatcat:3dud2qg52vgl5nyqqeglrybt5e
*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. ...##
###
Feasible Automata for Two-Variable Logic with Successor on Data Words
[chapter]

2012
*
Lecture Notes in Computer Science
*

They can be characterized by the extension of EMSO 2 (+1, ∼)

doi:10.1007/978-3-642-28332-1_30
fatcat:5pods2csn5e7zdr53mgtekqv6m
*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] . ...##
###
Order-Invariance of Two-Variable Logic is Decidable
[article]

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*...

##
###
Two-variable logic and key constraints on data words

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

doi:10.1145/1938551.1938571
dblp:conf/icdt/NiewerthS11
fatcat:nge44rsfvjb3tgrphosgncoyfe
*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. ...##
###
Satisfiability for two-variable logic with two successor relations on finite linear orders
[article]

2013
*
arXiv
*
pre-print

We show that the problem is decidable

arXiv:1204.2495v3
fatcat:hvc3msmleff4dbcmthkvfhttnq
*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*. ...##
###
Reasoning About Actions Using Description Logics with General TBoxes
[chapter]

2006
*
Lecture Notes in Computer Science
*

However, existing DL action formalisms fail to include general TBoxes, which

doi:10.1007/11853886_23
fatcat:25bxiylhjzhhnm3j6dsx5obobe
*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). ...##
###
Extending Büchi Automata with Constraints on Data Values
[article]

2012
*
arXiv
*
pre-print

These

arXiv:1012.5439v2
fatcat:wzw65wkzlnfqhfduuendca5a2u
*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. ...##
###
DL Actions with GCIs: a Pragmatic Approach

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 ...

##
###
Atomic Set Constraints with Projection
[chapter]

2002
*
Lecture Notes in Computer Science
*

This class subsumes some already studied classes such as atomic

doi:10.1007/3-540-45610-4_22
fatcat:snstgyv7bvgtbjjc3pvqnnfdv4
*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*. ...##
###
On Quantified Propositional Logics and the Exponential Time Hierarchy

2016
*
Electronic Proceedings in Theoretical Computer Science
*

We show that DQBF formulae correspond naturally to quantified propositional dependence logic and present a general

doi:10.4204/eptcs.226.14
fatcat:ab3al4k7mvdfdab6fnfgvbvsuu
*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. ...##
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Set constraints: Results, applications and future directions
[chapter]

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]. ...

##
###
Commutative Data Automata

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*. ...

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

1999
*
Lecture Notes in Computer Science
*

This combination can naturally be embedded into C 2 , the two variable fragment of predicate logic

doi:10.1007/3-540-48168-0_21
fatcat:a7f7ky3anzhkxi34zeqemtbq44
*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. ...
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