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V. Weispfenning (1999)
Mixed real-integer linear quantifier elimination
Bernard Boigelot, P. Wolper (2002)
Representing Arithmetic Constraints with Finite Automata: An Overview
J. Hopcroft, J. Ullman (1979)
Introduction to Automata Theory, Languages and Computation
Bernard Boigelot, S. Jodogne, P. Wolper (2003)
An Effective Decision Procedure for Linear Arithmetic with Integer and Real VariablesArXiv, cs.LO/0303019
R. Stansifer (1984)
Presburger''s Article on Integer Arithmetic: Remarks and Translation
T. Shiple, J. Kukula, R. Ranjan (1998)
A Comparison of Presburger Engines for EFSM Reachability
Bernard Boigelot, S. Jodogne, P. Wolper (2005)
An effective decision procedure for linear arithmetic over the integers and realsACM Trans. Comput. Log., 6
D. Oppen (1978)
A 2^2^2^pn Upper Bound on the Complexity of Presburger ArithmeticJ. Comput. Syst. Sci., 16
P. Wolper, Bernard Boigelot (1995)
An Automata-Theoretic Approach to Presburger Arithmetic Constraints (Extended Abstract)
Bernard Boigelot, S. Jodogne, P. Wolper (2001)
On the Use of Weak Automata for Deciding Linear Arithmetic with Integer and Real Variables
Alexei Semenov (1977)
Presburgerness of predicates regular in two number systemsSiberian Mathematical Journal, 18
· Felix Klaedtke
(2008)
ACM Transactions on Computational Logic
B. Sturmfels (2008)
Algorithms in Invariant Theory (Texts and Monographs in Symbolic Computation)
K. Reinhardt (2001)
The Complexity of Translating Logic to Finite Automata
U. Schöning (1997)
Complexity of presburger arithmetic with fixed quantifier dimensionTheory of Computing Systems, 30
J. Dixmier (1990)
Proof of a conjecture by Erdős and Graham concerning the problem of FrobeniusJournal of Number Theory, 34
(1972)
Theorem proving in arithmetic without multiplication
The Li`ege Automata-based Symbolic Handler
E. Grädel (1988)
Subclasses of Presburger Arithmetic and the Polynomial-Time HierarchyTheor. Comput. Sci., 56
B. Caviness, Jeremy Johnson (2004)
Quantifier Elimination and Cylindrical Algebraic Decomposition
J. Brzozowski, E. Leiss (1980)
On Equations for Regular Languages, Finite Automata, and Sequential NetworksTheor. Comput. Sci., 10
L. Berman (1980)
The Complexity of Logical TheoriesTheor. Comput. Sci., 11
Vijay Ganesh, S. Berezin, D. Dill (2002)
Deciding Presburger Arithmetic by Model Checking and Comparisons with Other Methods
C. Reddy, D. Loveland (1978)
Presburger arithmetic with bounded quantifier alternationProceedings of the tenth annual ACM symposium on Theory of computing
R. Nelson (1968)
Introduction to Automata
T. Rybina, A. Voronkov (2000)
A decision procedure for term algebras with queuesProceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)
Achim Blumensath, E. Grädel (2000)
Automatic structuresProceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)
T. Rybina, A. Voronkov (2003)
Upper Bounds for a Theory of Queues
Bernard Boigelot, Stéphane Rassart, P. Wolper (1998)
On the Expressiveness of Real and Integer Arithmetic Automata (Extended Abstract)
Bernard Boigelot (1998)
Symbolic Methods for Exploring Infinite State Spaces
M. Fischer, M. Rabin (1974)
SUPER-EXPONENTIAL COMPLEXITY OF PRESBURGER ARITHMETIC
(1930)
Uber die Vollständigkeit eines gewissen Systems der Arithmetik ganzer
(1988)
of the 4 th International Conference on Formal Methods in Computer - Aided Design ( FMCAD ’ 02 )
Véronique Bruyàre, G. Hansel, C. Michaux, Roger Villemaire (1994)
LOGIC AND p-RECOGNIZABLE SETS OF INTEGERSBulletin of The Belgian Mathematical Society-simon Stevin, 1
Tuba Yavuz-Kahveci, Constantinos Bartzis, T. Bultan (2005)
Action Language Verifier, Extended
Hubert Comon-Lundh (1995)
Linear diophantine equations, Presburger arithmetic and finite automata
J. Büchi (1960)
Weak Second‐Order Arithmetic and Finite AutomataMathematical Logic Quarterly, 6
(2008)
Article 11, Publication date
Presburger Arithmeticand, A. Boudet, Hubert ComonLRI (2007)
Finite Automata ?
L. Stockmeyer (1974)
The complexity of decision problems in automata theory and logic
J. Hopcroft (1971)
An n log n algorithm for minimizing states in a finite automaton
B. Khoussainov, A. Nerode (1994)
Automatic Presentations of Structures
(1970)
einige Satzfunktionen in der Arithmetik
P. Wolper, Bernard Boigelot (2000)
On the Construction of Automata from Linear Arithmetic Constraints
Constantinos Bartzis, T. Bultan (2003)
Efficient Symbolic Representations for Arithmetic Constraints in VerificationInt. J. Found. Comput. Sci., 14
A. Cobham (1969)
On the base-dependence of sets of numbers recognizable by finite automataMathematical systems theory, 3
Felix Klaedtke (2004)
On the automata size for Presburger arithmeticProceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
J. Ferrante, C. Rackoff (1979)
The computational complexity of logical theories
(1929)
in welchem die Addition als einzige Operation hervortritt
(2005)
Received June
(2003)
FAST: Fast accelereation of symbolic transition systems
J. Ferrante, C. Rackoff (1975)
A Decision Procedure for the First Order Theory of Real Addition with OrderSIAM J. Comput., 4
A. Chandra, Dexter Kozen, L. Stockmeyer (1981)
AlternationJ. ACM, 28
Automata provide a decision procedure for Presburger arithmetic. However, until now only crude lower and upper bounds were known on the sizes of the automata produced by the automata-based approach for Presburger arithmetic. In this article, we give an upper bound on the number of states of the minimal deterministic automaton for a Presburger arithmetic formula. This bound depends on the length of the formula and the quantifiers occurring in it. We establish the upper bound by comparing the automata for Presburger arithmetic formulas with the formulas produced by a quantifier-elimination method. We show that our bound is tight, also for nondeterministic automata. Moreover, we provide automata constructions for atomic formulas and establish lower bounds for the automata for linear equations and inequations.
ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery
Published: Mar 1, 2008
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