Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929.

This approach is the basis of at least five proof-of-correctness systems for computer programs, beginning with the Stanford Pascal Verifier in the late 1970s and continuing through to Microsoft's Spec# system of 2005. ==Presburger-definable integer relation== Some properties are now given about integer relations definable in Presburger Arithmetic.

C., 1972, "Theorem Proving in Arithmetic without Multiplication" in B.

Loveland, 1978, "Presburger Arithmetic with Bounded Quantifier Alternation." ACM Symposium on Theory of Computing: 320–325. Young, P., 1985, "Gödel theorems, exponential difficulty and undecidability of arithmetic theories: an exposition" in A.

Loveland, 1978, "Presburger Arithmetic with Bounded Quantifier Alternation." ACM Symposium on Theory of Computing: 320–325. Young, P., 1985, "Gödel theorems, exponential difficulty and undecidability of arithmetic theories: an exposition" in A.

Springer-Verlag. , see for an English translation William Pugh, 1991, "The Omega test: a fast and practical integer programming algorithm for dependence analysis,". Reddy, C.

This approach is the basis of at least five proof-of-correctness systems for computer programs, beginning with the Stanford Pascal Verifier in the late 1970s and continuing through to Microsoft's Spec# system of 2005. ==Presburger-definable integer relation== Some properties are now given about integer relations definable in Presburger Arithmetic.

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