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...e (correct) programs in the benchmark in about 10s of total time. Related Work Our work is influenced by recent advances in automatic static inference of inductive invariants using constraint solving =-=[6,14,26]-=- as well as by the use of dynamic analysis to estimate and infer likely system properties [9]. Constraint-based invariant synthesis techniques using templates in linear [2, 5, 14] and polynomial [20, ...

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...es in program verification indicate that various problems, for instance, termination analysis of linear programs [37], reachability computation of linear hybrid systems [28], and invariant generation =-=[19, 34]-=- can be reduced to solving semi-algebraic systems. Tools for real algebraic computation such as REDLOG [23] QEPCAD [18, 25, 6], and DISCOVERER [42] have therefore been applied to program verification ...

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...ear constraints only over the given set of expressions. There has been work on discovering restricted form of quadratic inequalities [5], polynomial inequality invariants [2], and equality invariants =-=[24, 21]-=- of bounded degree. In contrast, our domain lifting operation allows for discovering arbitrary polynomial inequalities as well as non-polynomial inequalities in a uniform setting, but over a given set...

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...omputing such invariants, and was shown to be sound and complete. However, that method cannot handle nested loops; furthermore, tests in conditional statements and loops are abstracted to be true. In =-=[22]-=-, a method is proposed for generating nonlinear polynomials as invariants, which starts with a template polynomial with undetermined coefficients and attempts to find values for the coefficients so th...

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...ected by other points at all. This results in a robust classifier which is not easily perturbed and leads to better predictability in results. There has been research on finding non-linear invariants =-=[25,20,23]-=-. These techniques aim at finding invariants which are restricted to polynomials of variables. In contrast, we are not generating non-linear predicates. We are finding linear over-approximations of no...

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...e assertions are the key to deductive verification of programs. Correspondingly, techniques for automatically checking and finding invariants and intermediate assertions have been studied (cf., e.g., =-=[3, 2, 22]-=-). In this paper we present analyses that check and find valid polynomial identities in programs. A polynomial identity is a formula p(x1, . . . , xk) = 0 where p(x1, . . . , xk) is a multi-variate po...

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...er is used to determine if there are inputs which cause the loop to execute infinitely. For linear programs with unbounded integers, TNT uses sophisticated invariant generation like that of [6], [7], =-=[8]-=- to find loop invariants that lead to non-termination and which hold for some program input. A backtracking nonlinear constraint solver is used to compute such an invariant. Although Gupta et al. focu...

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...s is not new. In fact, it is the classical approach used to prove stability in controlTALY, TIWARI FSTTCS 2009 3 theory. Recently, it has also been used for safety verification for discrete programs =-=[2, 7, 12, 19]-=- and continuous and hybrid systems [18, 16, 1, 21, 8]. These papers use templates for performing bounded verification, but differ in the details about their use of the inference rule to construct φ ′ ...