On probabilistic term rewriting

Martin Avanzini (1) , Ugo Dal Lago (2, 1) , Akihisa Yamada (3)

1 FOCUS - Foundations of Component-based Ubiquitous Systems
2 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
3 NII - National Institute of Informatics

We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite systems are considered. Two instances of the interpretation method—polynomial and matrix interpretations—are analyzed and shown to capture interesting and non trivial examples when automated. We capture probabilistic computation in a novel way by means of multidistribution reduction sequences, thus accounting for both the nondeterminism in the choice of the redex and the probabilism intrinsic in firing each rule.

Mots clés: Probabilistic term rewriting; Almost sure termination; Interpretation method; Probabilistic abstract reduction systems

Domaines: Complexité [cs.CC]

Martin Avanzini, Ugo Dal Lago, Akihisa Yamada. On probabilistic term rewriting. Science of Computer Programming, 2020, 185, pp.102338. ⟨10.1016/j.scico.2019.102338⟩. ⟨hal-02381877⟩