an:06052248
Zbl 1242.68196
Bonnet, R??mi; Finkel, Alain; Leroux, J??r??me; Zeitoun, Marc
Model checking vector addition systems with one zero-test
EN
Log. Methods Comput. Sci. 8, No. 2, Paper No. 11, 25 p. (2012).
00299640
2012
j
68R99 68Q05 03D99
vector addition system; zero-test; reachability; cover; boundedness; place boundedness; Karp-Miller algorithm; LTL model-checking
Summary: We design a variation of the Karp-Miller algorithm to compute, in a forward manner, a finite representation of the cover (i.e., the downward closure of the reachability set) of a vector addition system with one zero-test. This algorithm yields decision procedures for several problems for these systems, open until now, such as place-boundedness or LTL model-checking. The proof techniques to handle the zero-test are based on two new notions of cover: the refined and the filtered cover. The refined cover is a hybrid between the reachability set and the classical cover. It inherits properties of the reachability set: equality of two refined covers is undecidable, even for usual Vector Addition Systems (with no zero-test), but the refined cover of a vector addition system is a recursive set. The second notion of cover, called the filtered cover, is the central tool of our algorithms. It inherits properties of the classical cover, and in particular, one can effectively compute a finite representation of this set, even for vector addition systems with one zero-test.