Undecidability Results on Two-Variable Logics
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Complexity of Two-Variable Logic with Counting
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Two-variable logic with counting is decidable
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Small Substructures and Decidability Issues for First-Order Logic with Two Variables
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Complexity of the Two-Variable Fragment with Counting Quantifiers
Journal of Logic, Language and Information
Two-Variable Logic on Words with Data
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Two-variable logic on data trees and XML reasoning
Journal of the ACM (JACM)
On Finite Satisfiability of Two-Variable First-Order Logic with Equivalence Relations
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Two variables and two successors
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
The two-variable fragment with counting revisited
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
Two-variable logic with two order relations
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
On the complexity of the Bernays-Schönfinkel class with datalog
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Bounded model checking of pointer programs
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Two-Variable First-Order Logic with Equivalence Closure
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Complexity of two-variable logic on finite trees
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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We consider the two-variable logic with counting quantifiers (C2) interpreted over finite structures that contain two forests of ranked trees. This logic is strictly more expressive than standard C2 and it is no longer a fragment of the first order logic. In particular, it can express that a structure is a ranked tree, a cycle or a connected graph of bounded degree. It is also strictly more expressive than the first-order logic with two variables and two successor relations of two finite linear orders. We give a decision procedure for the satisfiability problem for this logic. The procedure runs in NEXPTIME, which is optimal since the satisfiability problem for plain C2 is NEXPTIME-complete.