Interprocedural Reachability for Flat Integer Programs

We study programs with integer data, procedure calls and arbitrary call graphs. We show that, whenever the guards and updates are given by octagonal relations, the reachability problem along control flow paths within some language w1* ... wd* over program statements is decidable in Nexptime. To achieve this upper bound, we combine a program transformation into the same class of programs but without procedures, with an Np-completeness result for the reachability problem of procedure-less programs. Besides the program, the expression w1* ... wd* is also mapped onto an expression of a similar form but this time over the transformed program statements. Several arguments involving context-free grammars and their generative process enable us to give tight bounds on the size of the resulting expression. The currently existing gap between Np-hard and Nexptime can be closed to Np-complete when a certain parameter of the analysis is assumed to be constant.Comment: 38 pages, 1 figur

Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system