Fast Acceleration of Ultimately Periodic Relations

Abstract

Abstract. Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we describe an efficient algorithm for computing the transitive closures of difference bounds, octagonal and finite monoid affine relations. On the theoretical side, this framework provides a common solution to the acceleration problem, for all these three classes of relations. In practice, according to our experiments, the new method performs up to four orders of magnitude better than the previous ones, making it a promising approach for the verification of integer programs.

A Verification Toolkit for Numerical Transition Systems

“…The unifying component is the INTS library 5 , which defines the syntax of the INTS representation by providing a parser and a library of abstract syntax tree classes. For the purposes of this paper, the INTS syntax is considered to be a textual description of a control flow graph labeled by Presburger arithmetic formulae, as in Figure 1 ( [3] in a semi-algorithm computing the summary relation incrementally, by eliminating control states and composing incoming with outgoing relations. Eldarica verifier.…”

Witness Runs for Counter Machines

“…Then, for every flat Presburger counter system from C, the reachability relation Reach C is Presburger-definable. This is at the heart of the decidability results for verifying safety and reachability properties on flat Presburger counter systems from [CJ98,FL02,BIK09] whereas for the verification of temporal properties, it is much more difficult to get sharp complexity characterization, see e.g. [DDS12].…”

“…A recent work unifying [CJ98, FL02, BGI09, BIL09] by considering all the families of formulae labelling transitions from these works can be found in [BIK09].…”

“…In general, computing the transitive closures of integer relations is a key step to solve verification problems on counter machines, see e.g. [BW94,CJ98,Fri00,FL02,BIK09].…”

“…Several classes of such flat operational devices have been identified and reachability sets have been shown effectively Presburger-definable for many of them, see e.g. [FO97,CJ98,Boi99,FL02,BIK09]. This provides a decision procedure for the reachability problem, given a prover for Presburger arithmetic validity.…”