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The complexity of semilinear problems in succinct representation
2006
Computational Complexity
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We prove completeness results for twenty-three problems in semilinear geometry. These results involve semilinear sets given by additive circuits as input data. ...
One such result, the P NP [log] -completeness of deciding Zariski irreducibility, exhibits for the first time a problem with a geometric nature complete in this class. ...
The first and third author would like to thank the Department of Mathematics and the Liu Bie Ju Centre for Mathematical Sciences of the City University of Hong Kong for the hospitality in April-June 2004 ...
doi:10.1007/s00037-006-0213-6
fatcat:n7so5dhq6bep7ob5eplfkpec5y
The Complexity of Semilinear Problems in Succinct Representation
[chapter]
2005
Lecture Notes in Computer Science
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We prove completeness results for twenty-three problems in semilinear geometry. These results involve semilinear sets given by additive circuits as input data. ...
One such result, the P NP[log] -completeness of deciding Zariski irreducibility, exhibits for the first time a problem with a geometric nature complete in this class. ...
The first and third author would like to thank the Department of Mathematics and the Liu Bie Ju Centre for Mathematical Sciences of the City University of Hong Kong for the hospitality in April-June 2004 ...
doi:10.1007/11537311_42
fatcat:cmnctwo6mfhivljqyl2jnt5nl4
Page 8666 of Mathematical Reviews Vol. , Issue 2003k
[page]
2003
Mathematical Reviews
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The worst-case complexity of the algorithms is similar to that in the static case. ...
So the problem of path-finding becomes a problem of finding a piecewise linear time- dependent trajectory of the given semilinear object from a given initial position to a semilinear set of admissible ...
Page 5320 of Mathematical Reviews Vol. , Issue 82m
[page]
1982
Mathematical Reviews
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The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
of the
equivalence problem for semilinear sets (double exponential time). ...
a fixed, finite number of times (reversal-bounded counters); (2) a determination of the complexity of the equivalence problem for such machines
(exponential time); (3) a determination of the complexity ...
Parikh Images of Regular Languages: Complexity and Applications
[article]
2010
arXiv
pre-print
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Previously, it was not known whether the number of generators could be made independent of n, and best upper bounds on the total size were exponential in n. ...
Our proof exploits a previously unknown connection to the theory of convex sets, and establishes a normal form theorem for semilinear sets, which is of independent interests. ...
The issues of succinctness and complexity of translations among different representations are also equally important. ...
arXiv:1002.1464v2
fatcat:6mj3yidpgrgmrpdd44dbmebbqa
Parikh Images of Grammars: Complexity and Applications
2010
2010 25th Annual IEEE Symposium on Logic in Computer Science
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In this paper, we study the complexity of Parikh's Theorem over any fixed alphabet size d. We prove various normal form theorems in the case of NFAs and CFGs. ...
In particular, the normal form theorems ensure that a union of linear sets with d generators suffice to express such Parikh images, which in the case of NFAs can further be computed in polynomial time. ...
The first author thanks Sławek Lasota for his introduction to these problems, and to everyone on the Automata Scientific Excursion for the great atmosphere of research. ...
doi:10.1109/lics.2010.21
dblp:conf/lics/KopczynskiT10
fatcat:ypefh6fzpbfvjkckma6iahk3hi
FPsolve: A Generic Solver for Fixpoint Equations over Semirings
[chapter]
2014
Lecture Notes in Computer Science
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We then succinctly describe some of the algorithms implemented in the tool, and provide some implementation details. ...
We introduce FPsolve, an implementation of generic algorithms for solving fixpoint equations over semirings. We first illustrate the interest of generic solvers by means of a scenario. ...
Acknowledgments We thank Michael Kerscher and Micha l Terepeta for their help in developing and extending FPsolve. ...
doi:10.1007/978-3-319-08846-4_1
fatcat:p6upw2gi5rhw7imt3urjyipd2m
The Complexity of Knapsack Problems in Wreath Products
2020
International Colloquium on Automata, Languages and Programming
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We prove new complexity results for computational problems in certain wreath products of groups and (as an application) for free solvable groups. ...
As an application of the latter, the power word problem for free solvable groups is in TC⁰. ...
126:16 The Complexity of Knapsack Problems in Wreath Products of the variables to elements of G (called EqnId(G) in [44] ) can be easily reduced to ∀-Sat(G). ...
doi:10.4230/lipics.icalp.2020.126
dblp:conf/icalp/FigeliusGLZ20
fatcat:ptqydcxlknaavoiyhgm42dofci
The finite embeddability property for residuated groupoids
2014
Algebra Universalis
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In particular, this gives an answer to the question posed in [3, Problem 4.2]. ...
The presented construction allows for improvement of the upper bound on the complexity of the decision procedure for the universal theory of residuated distributive-lattice-ordered groupoids, given in ...
Acknowledgment The work of the authors was supported by the grant P202/11/1632 of the Czech Science Foundation. ...
doi:10.1007/s00012-014-0284-1
fatcat:adsphbf7nncsfch2dpmy2txltu
Complexity of multi-head finite automata: Origins and directions
2011
Theoretical Computer Science
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It was proved in [1], where also an interesting connection with the open problem whether the computational complexity classes L = DSPACE(log n) and NL = NSPACE(log n) are equal is given. ...
Questions on the economics of description size were already investigated in the early days of theoretical computer science and build a cornerstone of descriptional complexity theory [39, 49, 58] . ...
So, it is natural to investigate the succinctness of their representation by different models. The regular languages are one of the first and most intensely studied language families. ...
doi:10.1016/j.tcs.2010.08.024
fatcat:yjkjor7r5rawrjijnxihcdnuve
On polynomial ideals, their complexity, and applications
[chapter]
1995
Lecture Notes in Computer Science
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We discuss complexity results known for a number of problems related to polynomial ideals, like the word problem for commutative semigroups, a quantitative version of Hilbert's Nullstellensatz, and the ...
A polynomial ideal membership problem is a (w+1)-tuple P = (f; g 1 ; g 2 ; : : : ; g w ) where f and the g i are multivariate polynomials over some ring, and the problem is to determine whether f is in ...
and term rewriting systems, tiling problems, the complexity of algebraic manifolds, and the complexity of some models for parallel systems. ...
doi:10.1007/3-540-60249-6_42
fatcat:soxs7hun4feqddpldpv2razz5y
Some Complexity Results for Polynomial Ideals
1997
Journal of Complexity
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In this paper, we survey some of our new results on the complexity of a number of problems related to polynomial ideals. ...
We discuss further complexity results for problems related to polynomial ideals, like the word and subword problems for commutative semigroups, a quantitative version of Hilbert's Nullstellensatz in a ...
In further constructions in [36] , the algorithm for the generalized subword problem is then used to obtain explicit semilinear representations of congruence classes in finitely presented commutative ...
doi:10.1006/jcom.1997.0447
fatcat:d3cz6pfw3za4disutcnitfvlsa
Parametric Identification of Temporal Properties
[chapter]
2012
Lecture Notes in Computer Science
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search in the parameter space. ...
Given a dense-time real-valued signal and a parameterized temporal logic formula with both magnitude and timing parameters, we compute the subset of the parameter space that renders the formula satisfied ...
In other words, the set S consists of a representative sample of the optimal trade-offs available in the problem. ...
doi:10.1007/978-3-642-29860-8_12
fatcat:i4kbitjpg5ajhakezv6dbic4om
Presburger arithmetic with stars, rational subsets of graph groups, and nested zero tests
2019
2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
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In particular, this enables us to obtain a complete description of the complexity landscape of the rational subset membership problem for fixed graph groups: If the graph is a clique, the problem is NL-complete ...
Moreover, we consider for each problem a variant with a fixed parameter: We fix the star-height in the logic, a graph parameter for the membership problem, and the number of distinct zero-tests in the ...
We are indebted to Markus Lohrey for fruitful discussions about graph groups, some of which provided key insights that found their way into the present paper. ...
doi:10.1109/lics.2019.8785850
dblp:conf/lics/HaaseZ19
fatcat:luvx6cwuzbfnvp2kfmd7peo7ua
Multi-Head Finite Automata: Characterizations, Concepts and Open Problems
2009
Electronic Proceedings in Theoretical Computer Science
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2009 pre-print arXiv:0906.3051v1 fatcat:3gzcsrovffgdpkckdfsvumv2ci
In the present paper, we tour a fragment of this literature. ...
, the borderline between decidable and undecidable problems. ...
Descriptional Complexity It is natural to investigate the succinctness of the representations of formal languages by different models. ...
doi:10.4204/eptcs.1.9
fatcat:gdxlz36uczhghkxhtxhiatw2ja
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