A Robust Theory of Series Parallel Graphs
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 t...
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| Vydáno v: | Proceedings of ACM on programming languages Ročník 7; číslo POPL; s. 1058 - 1088 |
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09.01.2023
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| Abstract | 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, called synchronized 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 of counting complexity that is distinct from the classical notion of state complexity. The determinization construction translates a nondeterministic automaton with n states and k counting complexity to a deterministic automaton with 2n2 states and kn counting 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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| AbstractList | 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, called synchronized 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 of counting complexity that is distinct from the classical notion of state complexity. The determinization construction translates a nondeterministic automaton with n states and k counting complexity to a deterministic automaton with 2 n 2 states and kn counting 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. 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, called synchronized 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 of counting complexity that is distinct from the classical notion of state complexity. The determinization construction translates a nondeterministic automaton with n states and k counting complexity to a deterministic automaton with 2n2 states and kn counting 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. |
| ArticleNumber | 37 |
| Author | Stanford, Caleb Watson, Christopher Alur, Rajeev |
| Author_xml | – sequence: 1 givenname: Rajeev orcidid: 0000-0003-1733-7083 surname: Alur fullname: Alur, Rajeev email: alur@cis.upenn.edu organization: University of Pennsylvania, USA – sequence: 2 givenname: Caleb orcidid: 0000-0002-8428-7736 surname: Stanford fullname: Stanford, Caleb email: castan@cis.upenn.edu organization: University of California at San Diego, USA / University of California at Davis, USA – sequence: 3 givenname: Christopher orcidid: 0000-0003-3716-516X surname: Watson fullname: Watson, Christopher email: ccwatson@seas.upenn.edu organization: University of Pennsylvania, USA |
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On the Model Checking of the Graded μ -calculus on Tree e_1_2_1_60_1 e_1_2_1_20_1 e_1_2_1_41_1 e_1_2_1_24_1 e_1_2_1_45_1 e_1_2_1_62_1 e_1_2_1_22_1 e_1_2_1_43_1 e_1_2_1_64_1 e_1_2_1_28_1 e_1_2_1_49_1 e_1_2_1_26_1 e_1_2_1_47_1 e_1_2_1_31_1 e_1_2_1_54_1 e_1_2_1_8_1 e_1_2_1_56_1 e_1_2_1_6_1 e_1_2_1_12_1 e_1_2_1_35_1 e_1_2_1_50_1 e_1_2_1_4_1 e_1_2_1_10_1 e_1_2_1_33_1 e_1_2_1_52_1 e_1_2_1_2_1 e_1_2_1_16_1 e_1_2_1_39_1 e_1_2_1_14_1 e_1_2_1_37_1 e_1_2_1_58_1 e_1_2_1_18_1 Walukiewicz Igor (e_1_2_1_66_1) e_1_2_1_42_1 e_1_2_1_65_1 e_1_2_1_40_1 e_1_2_1_23_1 e_1_2_1_46_1 e_1_2_1_61_1 e_1_2_1_21_1 e_1_2_1_44_1 e_1_2_1_63_1 e_1_2_1_27_1 e_1_2_1_25_1 e_1_2_1_48_1 e_1_2_1_29_1 Engelfriet Joost (e_1_2_1_32_1) 2015 e_1_2_1_7_1 e_1_2_1_30_1 e_1_2_1_55_1 e_1_2_1_5_1 e_1_2_1_57_1 e_1_2_1_3_1 e_1_2_1_13_1 e_1_2_1_34_1 e_1_2_1_51_1 e_1_2_1_1_1 e_1_2_1_11_1 e_1_2_1_53_1 e_1_2_1_17_1 e_1_2_1_38_1 e_1_2_1_15_1 e_1_2_1_36_1 e_1_2_1_59_1 e_1_2_1_9_1 e_1_2_1_19_1 |
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| SSID | ssj0001934839 |
| Score | 2.22796 |
| Snippet | Motivated by distributed data processing applications, we introduce a class of labeled directed acyclic graphs constructed using sequential and parallel... |
| SourceID | crossref acm |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 1058 |
| SubjectTerms | Data streaming Formal languages and automata theory Information systems Theory of computation |
| SubjectTermsDisplay | Information systems -- Data streaming Theory of computation -- Formal languages and automata theory |
| Title | A Robust Theory of Series Parallel Graphs |
| URI | https://dl.acm.org/doi/10.1145/3571230 |
| Volume | 7 |
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