Incremental Minimization of Symbolic Automata
- 16 Downloads
Symbolic automata are generalizations of finite automata that have symbolic predicates over the alphabet as transitions instead of symbols. Recently, traditional automata minimization techniques have been generalized to symbolic automata. In this paper, we generalize the incremental minimization algorithm to symbolic automata such that the algorithm can be halted at any point for obtaining a partially minimized automaton. Instead of computing the sets of equivalence classes, the incremental algorithm checks for equivalence between pairs of states and if they are equivalent, merges them into a single state. We evaluate our algorithm on SFAs corresponding to Unicode regular expressions and compare them to the state-of-the-art symbolic automata minimization implementations.
The authors would like to thank anonymous reviews for their feedback. The work done in this paper is based upon work supported by the National Science Foundation (NSF) under grant numbers CNS 1739936, 1935724. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of NSF.
- 1.Regexlib. http://www.regexlib.com/
- 2.Almeida, M., Moreira, N., Reis, R.: On the performance of automata minimization algorithms. In: Proceedings of the 4th Conference on Computation in Europe: Logic and Theory of Algorithms, pp. 3–14 (2007)Google Scholar
- 4.Brzozowski, J.A.: Canonical regular expressions and minimal state graphs for definite events. Math. Theory Automata 12(6), 529–561 (1962)Google Scholar
- 5.D’Antoni, L., Veanes, M.: Minimization of symbolic automata. In: ACM SIGPLAN Notices, vol. 49, pp. 541–553. ACM (2014)Google Scholar
- 7.D’Antoni, L.: Symbolicautomata. https://github.com/lorisdanto/symbolicautomata/. Accessed 30 Oct 2017
- 10.Hartmanis, J.: Algebraic structure theory of sequential machines (prentice-hall international series in applied mathematics) (1966)Google Scholar
- 11.Hopcroft, J.: An n log n algorithm for minimizing states in a finite automaton. In: Theory of Machines and Computations, pp. 189–196, Elsevier (1971)Google Scholar
- 16.Veanes, M., De Halleux, P., Tillmann, N.: Rex: symbolic regular expression explorer. In: International Conference on Software Testing, Verification and Validation, pp. 498–507. IEEE (2010)Google Scholar
- 18.Watson, B.W.: An incremental DFA minimization algorithm. In: International Workshop on Finite-State Methods in Natural Language Processing, Helsinki, Finland (2001)Google Scholar