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Motivated by distributed data processing applications, we introduce a class of labeled directed acyclic graphs constructed using sequential and parallel composition operations, and study automata and logics over them. We show that deterministic and non-deterministic acceptors over such graphs have the same expressive power, which can be equivalently characterized by Monadic Second-Order logic and the graded µ-calculus. We establish closure under composition operations and decision procedures for membership, emptiness, and inclusion. A key feature of our graphs, calledsynchronized series-parallel graphs(SSPG), is that parallel composition introduces a synchronization edge from the newly introduced source vertex to the sink. The transfer of information enabled by such edges is crucial to the determinization construction, which would not be possible for the traditional definition of series-parallel graphs. SSPGs allow both ordered ranked parallelism and unordered unranked parallelism. The latter feature means that in the corresponding automata, the transition function needs to account for an arbitrary number of predecessors by counting each type of state only up to a specified constant, thus leading to a notion ofcounting complexitythat is distinct from the classical notion of state complexity. The determinization construction translates a nondeterministic automaton withnstates andkcounting complexity to a deterministic automaton with 2n2states andkncounting complexity, and both these bounds are shown to be tight. Furthermore, for nondeterministic automata a bound of 2 on counting complexity suffices without loss of expressiveness.
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Divide-and-Conquer Determinization of Büchi Automata Based on SCC Decomposition
The determinization of a nondeterministic Büchi automaton (NBA) is a fundamental construction of automata theory, with applications to probabilistic verification and reactive synthesis. The standard determinization constructions, such as the ones based on the Safra-Piterman’s approach, work on the whole NBA. In this work we propose a divide-and-conquer determinization approach. To this end, we first classify the strongly connected components (SCCs) of the given NBA as inherently weak, deterministic accepting, and nondeterministic accepting. We then present how to determinize each type of SCC independently from the others; this results in an easier handling of the determinization algorithm that takes advantage of the structure of that SCC. Once all SCCs have been determinized, we show how to compose them so to obtain the final equivalent deterministic Emerson-Lei automaton, which can be converted into a deterministic Rabin automaton without blow-up of states and transitions. We implement our algorithm in our tool COLA and empirically evaluate COLA with the state-of-the-art tools Spot and Owl on a large set of benchmarks from the literature. The experimental results show that our prototype COLA outperforms Spot and Owl regarding the number of states and transitions.
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- Award ID(s):
- 1704883
- PAR ID:
- 10391914
- Date Published:
- Journal Name:
- Book cover Book cover International Conference on Computer Aided Verification
- Page Range / eLocation ID:
- 152-173
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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