From Sequential Extended Regular Expressions to NFA with Symbolic Labels

Practical property specification languages such as the IEEE standard PSL use at their core Sequential Extended Regular Expressions (SERE). In order to enable the reuse of traditional verification techniques, it is necessary to translate SEREs into automata. SERE are regular expressions built over alphabets resulting from the state variables of the design under analysis. Thus, a traditional approach to generate the automaton would suffer from the fact that the size of the alphabet is exponential in the number of symbols in the design. In this work, we tackle this problem by proposing non-deterministic finite automata with symbolic representation of transitions labels, by way of propositional formulas, while states and transitions are explicitly represented. We provide a symbolic version of the algorithms for all the major operations over nondeterministic finite automata. The approach has been implemented in the AUTLIB library, with Binary Decision Diagrams (BDD) used to represent transition labels. We carried out a thorough experimental evaluation over a set of realistic benchmarks, comparing our library against MONA (which uses deterministic finite automata with BDD-based symbolic transitions), and against GRAZ (which features non-deterministic finite automata with a DNF-based representation of the labels). Experimental results over a realistic set of benchmarks show that both features of AUTLIB (the ability to deal with non-determinism, and a BDD-based treatment of labels) are fundamental to achieve acceptable performance.