TARZAN: A Region-Based Library for Forward and Backward Reachability of Timed Automata (Extended Version)
Andrea Manini, Matteo Rossi, Pierluigi San Pietro
TL;DR
Timed automata verification suffers from infinite state spaces; Tarzan addresses this by introducing a region-based abstraction that jointly tracks the order clocks become unbounded and preserves fractional-part orderings for bounded clocks. The core method is a refined region representation with ordered clock partitions, supported by algorithms for forward and backward reachability, and a formal complexity analysis including a bound of at most $3$ immediate delay predecessors per region when unbounded-order is tracked. Empirical evaluation across punctual-guard and closed TA shows Tarzan achieving superior performance relative to zone-based tools in those subclasses, while large constants still favor zones; backward reachability is demonstrated as practical for safety properties and Timed Games. The work provides a practical, extensible library that complements Uppaal/TChecker, with future work aimed at zone integration, networked backward analysis, and hybrid methods.
Abstract
The zone abstraction, widely adopted for its notable practical efficiency, is the de facto standard in the verification of Timed Automata (TA). Nonetheless, region-based abstractions have been shown to outperform zones in specific subclasses of TA. To complement and support mature zone-based tools, we introduce TARZAN, a C++ region-based verification library for TA. The algorithms implemented in TARZAN use a novel region abstraction that tracks the order in which clocks become unbounded. This additional ordering induces a finer partitioning of the state space, enabling backward algorithms to avoid the combinatorial explosion associated with enumerating all ordered partitions of unbounded clocks, when computing immediate delay predecessor regions. We validate TARZAN by comparing forward reachability results against the state-of-the-art tools Uppaal and TChecker. The experiments confirm that zones excel when TA have large constants and strict guards. In contrast, TARZAN exhibits superior performance on closed TA and TA with punctual guards. Finally, we demonstrate the efficacy of our backward algorithms, establishing a foundation for region-based analysis in domains like Timed Games, where backward exploration is essential.