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1
July 2018
LICS '18: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science
Publisher: ACM
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Citation Count: 0
Downloads (6 Weeks): 2, Downloads (12 Months): 17, Downloads (Overall): 17
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It is an open problem whether definability in Propositional Dynamic Logic (PDL) on forests is decidable. Based on an algebraic characterization by Bojańczyk, et. al., (2012) in terms of forest algebras, Straubing (2013) described an approach to PDL based on a kfold iterated distributive law. A proof that all languages ...
2
July 2018
Theory of Computing Systems: Volume 62 Issue 5, July 2018
Publisher: SpringerVerlag
The Parikh automaton model equips a finite automaton with integer registers and imposes a semilinear constraint on the set of their final settings. Here the theories of typed monoids and of rational series are used to characterize the language classes that arise algebraically. Complexity bounds are derived, such as containment ...
Keywords:
Automata, Circuits, Algebra, Monoids, Semilinear sets, Typed monoids
3
November 2017
ACM Transactions on Computational Logic (TOCL): Volume 18 Issue 4, December 2017
Publisher: ACM
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Downloads (6 Weeks): 2, Downloads (12 Months): 34, Downloads (Overall): 34
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We give an algebraic characterization, based on the bilateral semidirect product of finite monoids, of the quantifier alternation hierarchy in twovariable firstorder logic on finite words. As a consequence, we obtain a new proof that this hierarchy is strict. Moreover, by application of the theory of finite categories, we are ...
Keywords:
Identities, FO_{2}, J, Pseudovarities, Quantifier Alternation
4
May 2017
ACM SIGLOG News: Volume 4 Issue 2, April 2017
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 3, Downloads (12 Months): 23, Downloads (Overall): 66
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Complexity theory and the theory of regular languages both belong to the branch of computer science where the use of resources in computing is the main focus. However, they operate at different levels. While complexity theory seeks to classify computational problems by resource use, such as space and time, regular ...
5
December 2016
Computational Complexity: Volume 25 Issue 4, December 2016
Publisher: Birkhauser Verlag
The problem of determining whether several finite automata accept a word in common is closely related to the wellstudied membership problem in transformation monoids. We raise the issue of limiting the number of final states in the automata intersection problem. For automata with two final states, we show the problem ...
Keywords:
68Q15, 68Q17, 68Q25, NPcomplete, intersection problem, monoids, pointspread problem, 03D15, 68Q70, Finite automata, logspace
6
October 2016
ACM Transactions on Computation Theory (TOCT): Volume 9 Issue 1, December 2016
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 3, Downloads (12 Months): 16, Downloads (Overall): 85
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A proof system for a language L is a function f such that Range( f ) is exactly L . In this article, we look at proof systems from a circuit complexity point of view and study proof systems that are computationally very restricted. The restriction we study is proof ...
Keywords:
Proof complexity, circuit complexity, proof circuits, small depth proofs
7
July 2016
DLT 2016: Proceedings of the 20th International Conference on Developments in Language Theory  Volume 9840
Publisher: SpringerVerlag New York, Inc.
Logical formulas are naturally decomposed into their subformulas and circuits into their layers. How are these decompositions expressed in a purely languagetheoretical setting? We address that question, and in doing so, introduce a product directly on languages that parallels formula composition. This framework makes an essential use of languages of ...
Keywords:
Circuits, Logic, Hyperwords, Descriptive complexity, Languages
8
July 2016
LICS '16: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science
Publisher: ACM
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Citation Count: 0
Downloads (6 Weeks): 1, Downloads (12 Months): 20, Downloads (Overall): 46
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We study an extension of FO2[<], firstorder logic interpreted in finite words, in which formulas are restricted to use only two variables. We adjoin to this language twovariable atomic formulas that say, 'the letter a appears between positions x and y'. This is, in a sense, the simplest property that ...
9
January 2016
Theoretical Computer Science: Volume 610 Issue PA, January 2016
Publisher: Elsevier Science Publishers Ltd.
We give a method for specifying ultrafilter equations and identify their projections on the set of profinite words. Let B be the set of languages captured by firstorder sentences using unary predicates for each letter, arbitrary uniform unary numerical predicates and a predicate for the length of a word. We ...
Keywords:
Profinite equations, Regular languages, Ultrafilters, Formal languages, Stone duality
10
January 2016
Theoretical Computer Science: Volume 610 Issue PA, January 2016
Publisher: Elsevier Science Publishers Ltd.
We extend the # operator in a natural way and derive new types of counting complexity classes. While in the case of # C classes (where C could be some circuitbased class like NC 1 ) only proofs for acceptance of some input are being counted, one can also count ...
Keywords:
Branching programs, Arithmetization, Circuits, Counting
11
July 2015
LICS '15: Proceedings of the 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
Publisher: IEEE Computer Society
Bibliometrics:
Citation Count: 4
Downloads (6 Weeks): 0, Downloads (12 Months): 4, Downloads (Overall): 9
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12
April 2015
ACM Transactions on Computational Logic (TOCL): Volume 16 Issue 3, July 2015
Publisher: ACM
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Citation Count: 0
Downloads (6 Weeks): 2, Downloads (12 Months): 14, Downloads (Overall): 66
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Given two structures G and H distinguishable in FO k (firstorder logic with k variables), let A k ( G , H ) denote the minimum alternation depth of a FO k formula distinguishing G from H . Let A k ( n ) be the maximum value of A ...
Keywords:
Alternation hierarchy, finitevariable logic
13
September 2014
Designs, Codes and Cryptography: Volume 72 Issue 3, September 2014
Publisher: Kluwer Academic Publishers
We describe a new way to construct finite geometric objects. For every $$k$$ we obtain a symmetric configuration $$\mathcal{E }(k1)$$ with $$k$$ points on a line. In particular, we have a constructive existence proof for such configurations. The method is very simple and purely geometric. It also produces interesting periodic ...
Keywords:
Lexicographic codes, 05B15, Configurations, Projective planes, 51E15, Greedy algorithms
14
August 2013
Theoretical Computer Science: Volume 501, August, 2013
Publisher: Elsevier Science Publishers Ltd.
Following recent works that connect twovariable logic to circuits and monoids, as well as recent techniques for obtaining algebraic and logical characterizations of threshold circuits, we present an algebraic and logical characterization of the language recognition power of uniform linear threshold circuits. More specifically, for numerical predicate sets P satisfying ...
Keywords:
Linear ciruits, Weakly blocked monoids, Twovariable logic, Boundeddepth circuits
15
May 2013
ACM Transactions on Computation Theory (TOCT): Volume 5 Issue 1, May 2013
Publisher: ACM
Bibliometrics:
Citation Count: 1
Downloads (6 Weeks): 3, Downloads (12 Months): 14, Downloads (Overall): 137
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In this paper we initiate the study of proof systems where verification of proofs proceeds by NC 0 circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by NC 0 functions. Our results show that ...
Keywords:
Proof circuits, Proof complexity, small depth proofs, circuit complexity
16
October 2012
Algorithmica: Volume 64 Issue 2, October 2012
Publisher: SpringerVerlag New York, Inc.
We give a #NC 1 upper bound for the problem of counting accepting paths in any fixed visibly pushdown automaton. Our algorithm involves a nontrivial adaptation of the arithmetic formula evaluation algorithm of Buss, Cook, Gupta and Ramachandran (SIAM J. Comput. 21:755780, 1992). We also show that the problem is ...
17
October 2012
Algorithmica  Special Issue: Computing and Combinatorics: Volume 64 Issue 2, October 2012
Publisher: SpringerVerlag New York, Inc.
We give a #NC 1 upper bound for the problem of counting accepting paths in any fixed visibly pushdown automaton. Our algorithm involves a nontrivial adaptation of the arithmetic formula evaluation algorithm of Buss, Cook, Gupta and Ramachandran (SIAM J. Comput. 21:755–780, 1992). We also show that the problem is ...
18
August 2012
MFCS'12: Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Publisher: SpringerVerlag
The effect of severely tightening the uniformity of Boolean circuit families is investigated. The impact on NC 1 and its subclasses is shown to depend on the characterization chosen for the class, while classes such as P appear to be more robust. Tightly uniform subclasses of NC 1 whose separation ...
19
June 2012
LICS '12: Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Publisher: IEEE Computer Society
Bibliometrics:
Citation Count: 1
Downloads (6 Weeks): 1, Downloads (12 Months): 7, Downloads (Overall): 70
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We consider firstorder logic with monoidal quantifiers over words. We show that all languages with a neutral letter, definable using the addition predicate are also definable with the order predicate as the only numerical predicate. Let S be a subset of monoids. Let L be the logic closed under quantification ...
Keywords:
descriptive complexity, logic on words, cranebeach conjecture, extended firstorder logic
20
August 2011
MFCS'11: Proceedings of the 36th international conference on Mathematical foundations of computer science
Publisher: SpringerVerlag
We study the streaming complexity of the membership problem of 1turnDyck 2 and Dyck 2 when there are a few errors in the input string. 1turnDyck 2 with errors: We prove that there exists a randomized onepass algorithm that given x checks whether there exists a string x ′ ∈ ...

