Weak Arithmetic Completeness of Object-Oriented First-Order Assertion Networks

Abstract

Abstract. We present a completeness proof of the inductive assertion method for object-oriented programs extended with auxiliary variables. The class of programs considered are assumed to compute over structures which include the standard interpretation of Presburger arithmetic. Further, the assertion language is first-order, i.e., quantification only ranges over basic types like that of the natural numbers, Boolean and Object.

Integrating deductive verification and symbolic execution for abstract object creation in dynamic logic

“…It is not difficult though tedious to show that using auxiliary array variables we can express in our firstorder language strongest post-conditions for our programming language. In fact, in [23], we prove that the strongest post-condition of a formula in the language of Presburger arithmetic and a program instrumented with auxiliary variables in a suitable manner is definable in Presburger arithmetic itself. This is surprising, since the standard approach to show that the strongest post-condition is definable is based on the usual Gödel encoding of partial recursive functions, which relies on the presence of multiplication in the assertion language, and multiplication is not available in Presburger arithmetic.…”