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Weak Minimization of DFA — An Algorithm and Applications [chapter]

Bala Ravikumar
2003 Lecture Notes in Computer Science  
DFA minimization is an important problem in algorithm design and is based on the notion of DFA equivalence: Two DFA's are equivalent if and only if they accept the same set of strings.  ...  We illustrate, in the case of a tiling problem, that our algorithm reduces a (strongly minimal) DFA by a factor close to 1/2.  ...  Acknowledgements Some of the programs described above were implemented by Xiaoming Lu, a graduate student at Sonoma State University.  ... 
doi:10.1007/3-540-45089-0_21 fatcat:7xb4dduvirbqtgfzwmq3e5xskq

Weak minimization of DFA—an algorithm and applications

B. Ravikumar, G. Eisman
2004 Theoretical Computer Science  
DFA minimization is an important problem in algorithm design and is based on the notion of DFA equivalence: Two DFA's are equivalent if and only if they accept the same set of strings.  ...  We illustrate, in the case of a tiling problem, that our algorithm reduces a (strongly minimal) DFA by a factor close to 1/2.  ...  Acknowledgements Some of the programs described above were implemented by Xiaoming Lu, a graduate student at Sonoma State University.  ... 
doi:10.1016/j.tcs.2004.07.009 fatcat:crtbk4bnijextj4tl64rxcpvkm

Secure Finite Automaton: Equivalence, Determinization and Minimization

Pinghong Ren, Chu Chen, Yuanke Zhang, Jiguo Yu, Fengyin Li
2016 ICIC Express Letters  
Algorithms for determinizing and minimizing a secure finite automaton are given with proofs of correctness and analyses of the worst case time complexity.  ...  The application of these algorithms shows that this development is very useful.  ...  XJ201226, and the Program of Science and Technology (the Youth Foundation) of Qufu Normal University with Grant No. xkj201313.  ... 
doi:10.24507/icicel.10.11.2587 fatcat:6tarj7nqsjbhpjl5ex7vjln5ly

On the Power of Automata Minimization in Reactive Synthesis

Shufang Zhu, Lucas M. Tabajara, Geguang Pu, Moshe Y. Vardi
2021 Electronic Proceedings in Theoretical Computer Science  
Here, we present a thorough investigation on two classical minimization algorithms, namely, the Hopcroft and Brzozowski algorithms.  ...  We then compare the two algorithms in the context of an LTL f -synthesis framework, starting from LTL f formulas.  ...  IIS-1527668, CCF-1704883, IIS-1830549, DoD MURI grant N00014-20-1-2787, and an award from the Maryland Procurement Office.  ... 
doi:10.4204/eptcs.346.8 fatcat:65vawwmkczdkda35dzjl43jfnq

Hybrid Compositional Reasoning for Reactive Synthesis from Finite-Horizon Specifications

Suguman Bansal, Yong Li, Lucas Tabajara, Moshe Vardi
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
DFA but are slow due to expensive DFA minimization.  ...  In doing so, we offer an LTLf to DFA conversion technique that addresses all three necessities, hence resolving the bottleneck.  ...  By diligent application of both representations, our hybrid approach is able to leverage their complementary strengths and render an algorithm that is not only competitive time-and memorywise, but also  ... 
doi:10.1609/aaai.v34i06.6528 fatcat:pg4cs7cferbcvhkkwt3quqpl4i

Better Hyper-minimization [chapter]

Andreas Maletti
2011 Lecture Notes in Computer Science  
MFCS, LNCS 5734, 2009] and [Holzer and Maletti: An n log n algorithm for hyper-minimizing a (minimized) deterministic automaton. Theor. Comput. Sci. 411, 2010].  ...  In addition, an experimental study on random automata is performed and the effects of the existing algorithms and the new algorithm are reported.  ...  The equivalence class of an element s Algorithm 1 1 Structure of a hyper-minimization algorithm.  ... 
doi:10.1007/978-3-642-18098-9_22 fatcat:wx4zr6lal5eavfz7tr4igqr6ny

OPTIMAL HYPER-MINIMIZATION

ANDREAS MALETTI, DANIEL QUERNHEIM
2011 International Journal of Foundations of Computer Science  
Mfcs, Lncs 5734, 2009] and [Holzer and Maletti: An n log n algorithm for hyper-minimizing a (minimized) deterministic automaton. Theor. Comput. Sci. 411, 2010].  ...  In addition, an experimental study on random automata is performed and the effects of the existing algorithms and the new algorithm are reported.  ...  Acknowledgements The authors gratefully acknowledge the reviewers' comments. b The complete C ++ source code will be made available upon request, and the FSM<2.0> library is available at http://www.ling.uni-potsdam.de  ... 
doi:10.1142/s0129054111009094 fatcat:2jd3cp5za5dq3dlbcl5amtngdi

HYPER-MINIMIZATION IN O(n2)

ANDREW BADR
2009 International Journal of Foundations of Computer Science  
Second, our main result is a faster algorithm for the natural minimization problem: given a starting DFA D, find the smallest (by number of states) DFA D ′ such that L(D) and L(D ′ ) are f-equivalent.  ...  The study of f-equivalent languages, and particularly the DFAs that accept them, was recently introduced [1]. First, we restate the fundamental results in this new area of research.  ...  An obvious weakness of the DFCA is that its ability to remove the redundant computation necessitated by counting can only be applied to finite languages.  ... 
doi:10.1142/s012905410900684x fatcat:cgu32ar2e5hupc2ovwfaour26u

Penrose: Putting Compositionality to Work for Petri Net Reachability [chapter]

Paweł Sobociński, Owen Stephens
2013 Lecture Notes in Computer Science  
We introduce a tool that uses this technique, Penrose, discuss some design details in its implementation, and identify potential future improvements.  ...  DFA procedure; and further development of an algorithm for automatic decomposition of nets.  ...  Future work will investigate applying our decomposition technique to model checking problems other than reachability; optimising BDD representation, particularly w.r.t. the performance of the NFA to minimal  ... 
doi:10.1007/978-3-642-40206-7_29 fatcat:rbhhbfcszzdx7c3p5kqze3eggq

Hybrid Compositional Reasoning for Reactive Synthesis from Finite-Horizon Specifications [article]

Suguman Bansal, Yong Li, Lucas M. Tabajara, Moshe Y. Vardi
2020 arXiv   pre-print
DFA but are slow due to expensive DFA minimization.  ...  In doing so, we offer an LTLf to DFA conversion technique that addresses all three necessities, hence resolving the bottleneck.  ...  Wells and S. Zhu for their valuable inputs at different stages of the project.  ... 
arXiv:1911.08145v3 fatcat:xf5o7lrblnfwlbd6ioraln676a

On the Power of Automata Minimization in Temporal Synthesis [article]

Shufang Zhu, Lucas M. Tabajara, Geguang Pu, Moshe Y. Vardi
2020 arXiv   pre-print
This algorithm first constructs a DFA for the reverse language of the specification and then performs a series of operations to transform it into a minimal DFA for the specification itself.  ...  In this work we investigate DFA-minimization algorithms in the context of temporal synthesis.  ...  In this section, we describe how the algorithm can be adapted to construct a minimal DFA from an LTL f formula, presenting both an explicit and symbolic version of the algorithm.  ... 
arXiv:2008.06790v1 fatcat:eub57am5fvhrhnwl5mdwanq7wu

Private intersection of regular languages

Roberto Guanciale, Dilian Gurov, Peeter Laud
2014 2014 Twelfth Annual International Conference on Privacy, Security and Trust  
We discuss the various possibilities for solving the problem efficiently, and argue for an approach based on minimal deterministic finite automata (DFA) as a suitable, non-leaking representation of regular  ...  We propose two different algorithms for DFA minimization in a secure multiparty computation setting, illustrating different aspects of programming based on universal composability and the constraints this  ...  IUT27-1, and by ERDF through Centre of Excellence in Computer Science (EXCS).  ... 
doi:10.1109/pst.2014.6890930 dblp:conf/pst/GuancialeGL14 fatcat:mmd4c3vuura3dapg2zdp6flvly

Minimal partial languages and automata

Francine Blanchet-Sadri, K. Goldner, A. Shackleton
2017 RAIRO - Theoretical Informatics and Applications  
Our paper focuses on algorithms for the construction of minimal partial languages, associated with some -substitution, as well as approximation algorithms for the construction of minimal -DFAs.  ...  Partial words are sequences of characters from an alphabet in which some positions may be marked with a "hole" symbol, .  ...  Running standard DFA minimization algorithms on this -DFA results in an approximation of a minimal -DFA for L. Proposition 1. The language L σ output by Minlang satisfies σ(L σ ) = L.  ... 
doi:10.1051/ita/2017011 fatcat:3whyb3txcnhqtfuof5w2tvk5hm

Deciding Monadic Second Order Logic over $$\omega $$ ω -Words by Specialized Finite Automata [chapter]

Stephan Barth
2016 Lecture Notes in Computer Science  
Minimization of loop automata is basically the same as minimization of deterministic finite automata. Efficient minimization is an important feature for an efficient decision procedure for MSO.  ...  We developed an efficient algorithm for homomorphisms in this representation, which is essential for deciding MSO.  ...  The most mature implementation of any variant of MSO is MONA [8] , an implementation of the decision procedure for weak MSO over words and trees (wMSO, also WS1S and WS2S), a variant of MSO deciable by  ... 
doi:10.1007/978-3-319-33693-0_16 fatcat:5jhmpma5kfbmzaxvamtoejrkri

Learning Moore Machines from Input-Output Traces [article]

Georgios Giantamidis, Stavros Tripakis
2016 arXiv   pre-print
We develop three algorithms for solving this problem: (1) the PTAP algorithm, which transforms a set of input-output traces into an incomplete Moore machine and then completes the machine with self-loops  ...  Finally, we compare with OSTIA, an algorithm that learns a more general class of transducers, and find that OSTIA generally does not learn a Moore machine, even when fed with a characteristic sample.  ...  In the context of system design, an important problem, with numerous applications, is automatically generating models from data.  ... 
arXiv:1605.07805v2 fatcat:xvpb6do73rdpzmntaw3p67n4ki
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