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The complexity of semilinear problems in succinct representation

Peter Bürgisser, Felipe Cucker, Paulin Jacobé de Naurois
2006 Computational Complexity  
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]

Peter Bürgisser, Felipe Cucker, Paulin Jacobé de Naurois
2005 Lecture Notes in Computer Science  
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  
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  
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]

Anthony Widjaja To
2010 arXiv   pre-print
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

Eryk Kopczynski, Anthony Widjaja To
2010 2010 25th Annual IEEE Symposium on Logic in Computer Science  
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]

Javier Esparza, Michael Luttenberger, Maximilian Schlund
2014 Lecture Notes in Computer Science  
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

Michael Figelius, Moses Ganardi, Markus Lohrey, Georg Zetzsche, Emanuela Merelli, Artur Czumaj, Anuj Dawar
2020 International Colloquium on Automata, Languages and Programming  
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

Zuzana Haniková, Rostislav Horčík
2014 Algebra Universalis  
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

Markus Holzer, Martin Kutrib, Andreas Malcher
2011 Theoretical Computer Science  
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]

Ernst W. Mayr
1995 Lecture Notes in Computer Science  
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

Ernst W. Mayr
1997 Journal of Complexity  
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]

Eugene Asarin, Alexandre Donzé, Oded Maler, Dejan Nickovic
2012 Lecture Notes in Computer Science  
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

Christoph Haase, Georg Zetzsche
2019 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
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

Markus Holzer, Martin Kutrib, Andreas Malcher
2009 Electronic Proceedings in Theoretical Computer Science  
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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