Zenoness for Timed Pushdown Automata

Timed pushdown automata are pushdown automata extended with a finite set of real-valued clocks. Additionaly, each symbol in the stack is equipped with a value representing its age. The enabledness of a transition may depend on the values of the clocks and the age of the topmost symbol. Therefore, dense-timed pushdown automata subsume both pushdown automata and timed automata. We have previously shown that the reachability problem for this model is decidable. In this paper, we study the zenoness problem and show that it is EXPTIME-complete.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Weighted Pushdown Systems with Indexed Weight Domains

The reachability analysis of weighted pushdown systems is a very powerful technique in verification and analysis of recursive programs. Each transition rule of a weighted pushdown system is associated with an element of a bounded semiring representing the weight of the rule. However, we have realized that the restriction of the boundedness is too strict and the formulation of weighted pushdown systems is not general enough for some applications. To generalize weighted pushdown systems, we first introduce the notion of stack signatures that summarize the effect of a computation of a pushdown system and formulate pushdown systems as automata over the monoid of stack signatures. We then generalize weighted pushdown systems by introducing semirings indexed by the monoid and weaken the boundedness to local boundedness

Revisiting Underapproximate Reachability for Multipushdown Systems

Boolean programs with multiple recursive threads can be captured as pushdown automata with multiple stacks. This model is Turing complete, and hence, one is often interested in analyzing a restricted class that still captures useful behaviors. In this paper, we propose a new class of bounded under approximations for multi-pushdown systems, which subsumes most existing classes. We develop an efficient algorithm for solving the under-approximate reachability problem, which is based on efficient fix-point computations. We implement it in our tool BHIM and illustrate its applicability by generating a set of relevant benchmarks and examining its performance. As an additional takeaway, BHIM solves the binary reachability problem in pushdown automata. To show the versatility of our approach, we then extend our algorithm to the timed setting and provide the first implementation that can handle timed multi-pushdown automata with closed guards.Comment: 52 pages, Conference TACAS 202

The minimal cost reachability problem in priced timed pushdown systems

Abstract. This paper introduces the model of priced timed pushdown systems as an extension of discrete-timed pushdown systems with a cost model that assigns multidimensional costs to both transitions and stack symbols. For this model, we consider the minimal cost reachability problem: i.e., given a priced timed pushdown system and a target set of configurations, determine the minimal possible cost of any run from the initial to a target configuration. We solve the problem by reducing it to the reachability problem in standard pushdown systems.

時間プッシュダウンオートマトンの表現力と到達可能性問題

筑波大学 (University of Tsukuba)201