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On the Automata Size for Presburger Arithmetic
 In Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS 2004
, 2004
"... Automata provide an effective mechanization of decision procedures for Presburger arithmetic. However, only crude lower and upper bounds are known on the sizes of the automata produced by this approach. In this paper, we prove that the number of states of the minimal deterministic automaton for a Pr ..."
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Cited by 11 (1 self)
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Automata provide an effective mechanization of decision procedures for Presburger arithmetic. However, only crude lower and upper bounds are known on the sizes of the automata produced by this approach. In this paper, we prove that the number of states of the minimal deterministic automaton for a
Weakening Presburger Arithmetic
"... Abstract. We consider logics on Z and N which are weaker than Presburger Arithmetic and we settle the following decision problem: given a kary relation on Z and N which is first order definable in Presburger Arithmetic, is it definable in these weaker logics? These logics, intuitively, are obtained ..."
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Abstract. We consider logics on Z and N which are weaker than Presburger Arithmetic and we settle the following decision problem: given a kary relation on Z and N which is first order definable in Presburger Arithmetic, is it definable in these weaker logics? These logics, intuitively
SuperExponential Complexity of Presburger Arithmetic
, 1974
"... Lower bounds are established on the computational complexity of the decision problem and on the inherent lengths of proofs for two classical decidable theories of logic: the first order theory of the real numbers under addition, and Presburger arithmetic  the first order theory of addition on the ..."
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Cited by 121 (2 self)
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Lower bounds are established on the computational complexity of the decision problem and on the inherent lengths of proofs for two classical decidable theories of logic: the first order theory of the real numbers under addition, and Presburger arithmetic  the first order theory of addition
Bounds on the Automata Size for Presburger Arithmetic
, 2005
"... 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 this approach. In this paper, we prove an upper bound on the the number of states of the minimal deterministic automaton for a Pre ..."
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Cited by 5 (0 self)
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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 this approach. In this paper, we prove an upper bound on the the number of states of the minimal deterministic automaton for a
Presburger Arithmetic With Unary Predicates is ... Complete
 Journal of Symbolic Logic
, 1991
"... : We give a simple proof characterizing the complexity of Presburger arithmetic augmented with additional predicates. We show that Presburger arithmetic with additional predicates is \Pi 1 1 complete. Adding one unary predicate is enough to get \Pi 1 1 hardness, while adding more predicates (of an ..."
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Cited by 25 (1 self)
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: We give a simple proof characterizing the complexity of Presburger arithmetic augmented with additional predicates. We show that Presburger arithmetic with additional predicates is \Pi 1 1 complete. Adding one unary predicate is enough to get \Pi 1 1 hardness, while adding more predicates (of
Generic proof synthesis for Presburger arithmetic
, 2003
"... We develop in complete detail an extension of Cooperâ€™s decision procedure for Presburger arithmetic that returns a proof of the equivalence of the input formula to a quantifierfree formula. For closed input formulae this is a proof of their validity or unsatisfiability. The algorithm is formulated ..."
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Cited by 4 (3 self)
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We develop in complete detail an extension of Cooperâ€™s decision procedure for Presburger arithmetic that returns a proof of the equivalence of the input formula to a quantifierfree formula. For closed input formulae this is a proof of their validity or unsatisfiability. The algorithm is formulated
Complexity and Uniformity of Elimination in Presburger Arithmetic
 UNIVERSITAT PASSAU
, 1997
"... The decision complexity of Presburger Arithmetic PA and its variants has received much attention in the literature. We investigate the complexity of quantifier elimination procedures for PA  a topic that is even more relevant for applications. First we show that the the author's triply expone ..."
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Cited by 15 (3 self)
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The decision complexity of Presburger Arithmetic PA and its variants has received much attention in the literature. We investigate the complexity of quantifier elimination procedures for PA  a topic that is even more relevant for applications. First we show that the the author's triply
Deciding Boolean Algebra with Presburger Arithmetic
 J. of Automated Reasoning
"... Abstract. We describe an algorithm for deciding the firstorder multisorted theory BAPA, which combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmetic operations (PA). BAPA can express the relationship between integer variables and cardinalities of unbounded ..."
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Cited by 35 (27 self)
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Abstract. We describe an algorithm for deciding the firstorder multisorted theory BAPA, which combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmetic operations (PA). BAPA can express the relationship between integer variables and cardinalities of unbounded
Diophantine Equations, Presburger Arithmetic and Finite Automata
, 1996
"... . We show that the use of finite automata provides a decision procedure for Presburger Arithmetic with optimal worst case complexity. Introduction Solving linear equations and inequations with integer coefficients in the set Nof nonnegative integer plays an important role in many areas of computer ..."
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Cited by 84 (1 self)
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. We show that the use of finite automata provides a decision procedure for Presburger Arithmetic with optimal worst case complexity. Introduction Solving linear equations and inequations with integer coefficients in the set Nof nonnegative integer plays an important role in many areas
Results 1  10
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