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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
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
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
Multiple counters automata, safety analysis and Presburger arithmetic
, 1998
"... We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j +c i;j where y i is either x 0 i or ..."
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Cited by 117 (1 self)
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We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j +c i;j where y i is either x 0 i
On the use of nondeterministic automata for Presburger Arithmetic
"... Abstract. A wellknown decision procedure for Presburger arithmetic uses deterministic finitestate automata. While the complexity of the decision procedure for Presburger arithmetic based on quantifier elimination is known (roughly, there is a doubleexponential nondeterministic time lower bound ..."
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Abstract. A wellknown decision procedure for Presburger arithmetic uses deterministic finitestate automata. While the complexity of the decision procedure for Presburger arithmetic based on quantifier elimination is known (roughly, there is a doubleexponential nondeterministic time lower bound
Multiple counters automata, safety analysis and Presburger arithmetic
, 1998
"... . We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j + c i;j where y i is either x 0 i or ..."
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. We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j + c i;j where y i is either x 0 i
An AutomataTheoretic Approach to Presburger Arithmetic Constraints (Extended Abstract)
 In Proc. Static Analysis Symposium, LNCS 983
, 1995
"... This paper introduces a finiteautomata based representation of Presburger arithmetic definable sets of integer vectors. The representation consists of concurrent automata operating on the binary encodings of the elements of the represented sets. This representation has several advantages. First, be ..."
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Cited by 58 (5 self)
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This paper introduces a finiteautomata based representation of Presburger arithmetic definable sets of integer vectors. The representation consists of concurrent automata operating on the binary encodings of the elements of the represented sets. This representation has several advantages. First
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
On Presburger arithmetic extended with modulo counting quantifiers?
"... Abstract. We consider Presburger arithmetic (PA) extended with modulo counting quantifiers. We show that its complexity is essentially the same as that of PA, i.e., we give a doubly exponential space bound. This is done by giving and analysing a quantifier elimination procedure similar to Reddy an ..."
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Abstract. We consider Presburger arithmetic (PA) extended with modulo counting quantifiers. We show that its complexity is essentially the same as that of PA, i.e., we give a doubly exponential space bound. This is done by giving and analysing a quantifier elimination procedure similar to Reddy
Subclasses of Presburger arithmetic and the weak EXP hierarchy
 In Proc. CSLLICS
, 2014
"... ar ..."
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