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Language Equation Solving via Boolean Automata Manipulation

Published: 22 December 2022 Publication History

Abstract

Language equations are a powerful tool for compositional synthesis, modeled as the unknown component problem. Given a (sequential) system specification S and a fixed component F, we are asked to synthesize an unknown component X such that whose composition with F fulfills S. The synthesis of X can be formulated with language equation solving. Although prior work exploits partitioned representation for effective finite automata manipulation, it remains challenging to solve language equations involving a large number of states. In this work, we propose variants of Boolean automata as the underlying succinct representation for regular languages. They admit logic circuit manipulation and extend the scalability for solving language equations. Experimental results demonstrate the superiority of our method to the state-of-the-art in solving nine more cases out of the 36 studied benchmarks and achieving an average of 740× speedup.

References

[1]
Florent Avellaneda, Silvano Dal Zilio, and Jean-Baptiste Raclet. 2016. Solving Language Equations Using Flanked Automata. In International Symposium on Automated Technology for Verification and Analysis. 106--121.
[2]
Robert K. Brayton and Alan Mishchenko. 2010. ABC: An Academic Industrial-Strength Verification Tool. In Proceedings of the International Conference on Computer Aided Verification. 24--40.
[3]
Franc Brglez, David Bryan, and Krzysztof Kozminski. 1989. Combinational profiles of sequential benchmark circuits. In IEEE International Symposium on Circuits and Systems,. 1929--1934.
[4]
Janusz A. Brzozowski and Ernst Leiss. 1980. On equations for regular languages, finite automata, and sequential networks. Theoretical Computer Science 10, 1 (1980), 19--35.
[5]
Ashok K. Chandra, Dexter C. Kozen, and Larry J. Stockmeyer. 1981. Alternation. J. ACM 28, 1 (1981), 114--133.
[6]
Fulvio Corno, Matteo Sonza Reorda, and Giovanni Squillero. 2000. RT-level ITC'99 benchmarks and first ATPG results. IEEE Design & Test of Computers 17, 3 (2000), 44--53.
[7]
Arlen Cox and Jason Leasure. 2017. Model Checking Regular Language Constraints. CoRR abs/1708.09073 (2017). arXiv:1708.09073 http://arxiv.org/abs/1708.09073
[8]
A. Fellah, H. Jürgensen, and S. Yu. 1990. Constructions for alternating finite automata. International Journal of Computer Mathematics 35, 1--4 (1990), 117--132.
[9]
Minxi Gao, Jie-Hong R. Jiang, Yunjian Jiang, Yinghua Li, Alan Mishchenko, Subarna Sinha, Tiziano Villa, and Robert Brayton. 2002. Optimization of multivalued multi-level networks. In Proceedings of IEEE International Symposium on Multiple-Valued Logic. 168--177. https://ptolemy.berkeley.edu/projects/embedded/mvsis/
[10]
Priyanka Golia, Subhajit Roy, and Kuldeep S. Meel. 2020. Manthan: A Data-Driven Approach for Boolean Function Synthesis. In Proceedings of International Conference on Computer Aided Verification. 611--633.
[11]
Michal Hospodár, Galina Jirásková, and Ivana Krajňáková. 2018. Operations on Boolean and alternating finite automata. In Proceedings of International Computer Science Symposium in Russia. 181--193.
[12]
Galina Jirásková. 2012. Descriptional complexity of operations on alternating and Boolean automata. In Proceedings of International Computer Science Symposium in Russia. 196--204.
[13]
Alan Mishchenko, Robert Brayton, Roland Jiang, Tiziano Villa, and Nina Yevtushenko. 2005. Efficient solution of language equations using partitioned representations. In Proceedings of Design, Automation and Test in Europe Conference. 418--423.
[14]
Alan Mishchenko, Satrajit Chatterjee, Jie-Hong R. Jiang, and Robert K. Brayton. 2005. FRAIGs: A unifying representation for logic synthesis and verification. ERL Technical Report, UC Berkeley (2005).
[15]
Markus N. Rabe. 2019. Incremental determinization for quantifier elimination and functional synthesis. In Proceedings of International Conference on Computer Aided Verification. 84--94.
[16]
Íñigo X. Íncer Romeo, Leonardo Mangeruca, Tiziano Villa, and Alberto Sangiovanni-Vincentelli. 2020. The Quotient in Preorder Theories. Electronic Proceedings in Theoretical Computer Science 326 (sep 2020), 216--233.
[17]
Kai Salomaa, Xiuming Wu, and Sheng Yu. 2000. Efficient Implementation of Regular Languages Using Reversed Alternating Finite Automata. Theor. Comput. Sci. 231, 1 (2000), 103--111.
[18]
Michael Sipser. 1996. Introduction to the Theory of Computation. International Thomson Publishing.
[19]
Tiziano Villa, Alexandre Petrenko, Nina Yevtushenko, Alan Mishchenko, and Robert Brayton. 2015. Component-based design by solving language equations. Proc. IEEE 103, 11 (2015), 2152--2167.
[20]
Tiziano Villa, Nina Yevtushenko, Robert K. Brayton, Alan Mishchenko, Alexandre Petrenko, and Alberto Sangiovanni-Vincentelli. 2014. The Unknown Component Problem: Theory and Applications. Springer Publishing Company.
[21]
Hung-En Wang, Tzung-Lins Tsai, Chun-Han Lin, Fang Yu, and Jie-Hong R Jiang. 2016. String analysis via automata manipulation with logic circuit representation. In Proceedings of International Conference on Computer Aided Verification. 241--260.
[22]
Nina Yevtushenko, Tiziano Villa, Robert K. Brayton, Alex Petrenko, and Alberto L. Sangiovanni-Vincentelli. 2003. Sequential synthesis by language equation solving. Technical Report.

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cover image ACM Conferences
ICCAD '22: Proceedings of the 41st IEEE/ACM International Conference on Computer-Aided Design
October 2022
1467 pages
ISBN:9781450392174
DOI:10.1145/3508352
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 22 December 2022

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  • Ministry of Science and Technology of Taiwan

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ICCAD '22
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ICCAD '22: IEEE/ACM International Conference on Computer-Aided Design
October 30 - November 3, 2022
California, San Diego

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