2021/08/02 by Aneesh K. Shetty, Shetty, Aneesh K., Shankara Narayanan Krishna +3
Computer Science · #Distributed systems and fault tolerance #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Formal Methods in Verification #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2108.00963
openalex publication_date 2021/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Multi-pushdown systems are a standard model for concurrent recursive programs, but they have an undecidable reachability problem. Therefore, there have been several proposals to underapproximate their sets of runs so that reachability in this underapproximation becomes decidable. One such underapproximation that covers a relatively high portion of runs is scope boundedness. In such a run, after each push to stack i, the corresponding pop operation must come within a bounded number of visits to stack i. In this work, we generalize this approach to a large class of infinite-state systems. For this, we consider the model of valence systems, which consist of a finite-state control and an infinite-state storage mechanism that is specified by a finite undirected graph. This framework captures pushdowns, vector addition systems, integer vector addition systems, and combinations thereof. For this framework, we propose a notion of scope boundedness that coincides with the classical notion when the storage mechanism happens to be a multi-pushdown. We show that with this notion, reachability can be decided in PSPACE for every storage mechanism in the framework. Moreover, we describe the full complexity landscape of this problem across all storage mechanisms, both in the case of (i) the scope bound being given as input and (ii) for fixed scope bounds. Finally, we provide an almost complete description of the complexity landscape if even a description of the storage mechanism is part of the input.