Abstract
Visibly Pushdown Automata (VPAs) are a subclass of pushdown automata, which can be well applied as specification formalism for verification and the model for XML streams process. The input alphabet is partitioned into three disjoint sets: call, internal and return symbols, which can determine a push, pop or no stack operation taken by VPAs respectively. Hence, the matchings of push (call) and pop (return) make languages with matching nested relations accepted. Nevertheless, it is limited to one-to-one matching. In this paper, we extend the model of VPAs over multi-matching nested relations. By a subdivision for call and return symbols, inner-calls and inner-returns are obatined to discriminate a one-to-n or n-to-one matching relation. Then, Multi-matching Visibly Pushdown Automata (MVPA) are formally defined whose stack behavior is achieved by setting a guard in the stack, which can guarantee whether a one-to-n or n-to-one matching nested relation is read without confusion. Each nondeterministic multi-matching visibly pushdown automaton is demonstrated to be transformed into a deterministic one. Moreover, the symbolic version of multi-matching visibly pushdown automata is proposed when the input alphabet is given by a Boolean algebra where there is an infinite domain.
This research is supported by the NSFC Grant Nos. 62202371 and 61902312.
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References
Alur, R., Madhusudan, P.: Adding nesting structure to words. J. ACM (JACM) 56(3), 1–43 (2009)
Alur, R., Madhusudan, P.: Visibly pushdown languages. In: Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing, pp. 202–211 (2004)
Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, 2nd edn. Pearson Education, London (2000). ISBN 0-201-44124-1
Kumar, V., Madhusudan, P., Viswanathan, M.: Visibly pushdown automata for streaming XML. In: Proceedings of the 16th International Conference on World Wide Web (WWW 2007), 1053C1062 (2007)
Debarbieux, D., Gauwin, O., Niehren, J., et al.: Early nested word automata for XPath query answering on XML streams. Theor. Comput. Sci. 578, 100–125 (2015)
Chaudhuri, S., Alur, R.: Instrumenting C programs with nested word monitors. In: International SPIN Workshop on Model Checking of Software, pp. 279–283 (2007)
Driscoll, E., Thakur, A., Reps, T.: OpenNWA: a nested-word automaton library. In: International Conference on Computer Aided Verification, pp. 665–671 (2012)
Watson, B.W.: Implementing and using finite automata toolkits. In: Extended Finite State Models of Language, pp. 19–36. Cambridge University Press, New York (1999)
van Noord, G., Gerdemann, D.: Finite state transducers with predicates and identities. Grammars 4(3), 263–286 (2001)
D’Antoni, L., Alur, R.: Symbolic visibly pushdown automata. In: International Conference on Computer Aided Verification (CAV 2014), pp. 209–225 (2014)
Margus, V., Pieter, H., Benjamin, L., et al.: Symbolic finite state transducers: algorithms and applications. In: Proceedings of the 39th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL 2012), pp. 137–150 (2012)
Liu, J.. Duan, Z., Tian, C.: Transforming multi-matching nested traceable automata to multi-matching nested expressions. In: Proceedings of the 14th International Conference on Combinatorial Optimization and Applications (COCOA 2020), pp. 320–333 (2020)
Liu, J., Duan, Z., Tian, C.: Multi-matching nested relations. Theor. Comput. Sci. 854, 77–93 (2021)
Liu, J., Duan, Z., Tian, C.: Multi-matching nested languages. Chin. J. Electron. 31(1), 137–145 (2022)
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Liu, J., Xiao, Y., Wang, H., Wang, W. (2023). Extending Visibly Pushdown Automata over Multi-matching Nested Relations. In: Liu, S., Duan, Z., Liu, A. (eds) Structured Object-Oriented Formal Language and Method. SOFL+MSVL 2022. Lecture Notes in Computer Science, vol 13854. Springer, Cham. https://doi.org/10.1007/978-3-031-29476-1_5
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