Affine Loop Invariant Generation via Matrix Algebra

Abstract Loop invariant generation, which automates the generation of assertions that always hold at entry a while loop, has many important applications in program analysis and formal verification. In this work, we target an category loops, namely affine are unnested loops with loop guards variable updates. Such class widely exists programs yet still lacks general but efficient approach to generation. We propose novel matrix-algebra automatically synthesizing inductive invariants form inequality. The main novelty our is (i) sense it theoretically addresses all cases over (ii) can be efficiently automated through (such as eigenvalue, matrix inverse) methods. details follows. First, for case where guard tautology (i.e., ‘ true ’), show eigenvalues their eigenvectors matrices derived from updates body encompass meaningful invariants. Second, more conjunction inequalities, completely invariant-generation problem by first establishing inverse relationship between key parameter application Farkas’ lemma, then solving feasible domain conditions, finally illustrating finite number values suffices w.r.t tightness condition generated. Experimental results compared previous approaches, generates much accurate existing new benchmarks within few seconds, demonstrating generality efficiency approach.