Layered and Collecting NDFS with Subsumption for Parametric Timed Automata

Abstract

This paper studies the analysis and parameter synthesis problems for Parametric Timed Automata (PTA) with properties in Linear-time Temporal Logic (LTL). It introduces a series of variations of Nested Depth-First Search (NDFS). We first study the LTL model checking problem for PTA. Based on a careful analysis of parametric zones, we introduce a new layered NDFS approach to LTL model checking. We integrate this with several techniques to prune the search space. In particular, we apply subsumption abstraction to PTA for the first time. We also propose heuristics on the search order to improve the performance. Next, we study parameter synthesis. To this end, this new layered approach and subsumption are added to a Collecting NDFS scheme. We implemented all algorithms in the IMITATOR tool and analyse their efficiency in a number of experiments.

Iterative Bounded Synthesis for Efficient Cycle Detection in Parametric Timed Automata

“…In Sec. 4.1, we discuss the previous approach [11,25], based on Nested Depth-First Search (NDFS). All NDFS-based variants turn out to be incomplete for symbolic lassos.…”

“…Cumulative pruning (pink) [11,25]. For synthesis, we collect the Constraints that lead to accepting cycles (l.20).…”

“…2) A new synthesis algorithm, using bounded search with iterative deepening; this is the first algorithm that enumerates all accepting cycles in the possibly infinite PZG, in contrast to previous NDFS-based algorithms [25]. 3) An experimental benchmark, comparing the successful termination and runtime efficiency of all algorithms.…”

“…The basic cumulative algorithm [11] prunes states whose projected zone is already included in the accumulated constraint. The cumulative algorithm was extended with subsumption and layering for PTA [25]. The problem with all NDFS-based algorithms is that the computation can diverge in one branch, missing solutions for accepting cycles in other branches forever.…”

“…This way, we can reuse its PTA benchmark [4]. We also reimplemented the algorithms of [11,25] in a single NDFS framework. We illustrate our method on the Bounded Retransmission Protocol (BRP).…”