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Lowerbounds for Bisimulation by Partition Refinement [article]

Jan Friso Groote, Jan Martens, Erik. P. de Vink
2022 arXiv   pre-print
For sequential algorithms this is Ω((m 1mu +1mu n ) -1mu log-1mu n) and for parallel algorithms this is Ω(n), where n is the number of states and m is the number of transitions.  ...  We provide time lower bounds for sequential and parallel algorithms deciding bisimulation on labeled transition systems that use partition refinement.  ...  algorithm is ((m+n) log n).  ... 
arXiv:2203.07158v1 fatcat:ctwvc2yanjelta6q7elyarf6vq

A Fast Bisimulation Algorithm [chapter]

Agostino Dovier, Carla Piazza, Alberto Policriti
2001 Lecture Notes in Computer Science  
Starting from a set-theoretic point of view we propose an algorithm that optimizes the solution to the Relational coarsest Partition problem given by Paige and Tarjan in 1987 and its use in model-checking  ...  packages is briefly discussed and tested.  ...  The work is partially supported by MURST project: Certificazione automatica di programmi mediante interpretazione astratta.  ... 
doi:10.1007/3-540-44585-4_8 fatcat:5aqzt7b67ng63cn5iqc3gnchdi

Efficient Type Matching [chapter]

Somesh Jha, Jens Palsberg, Tian Zhao
2002 Lecture Notes in Computer Science  
Our result: We present an O(n log n) time algorithm for deciding the type equivalence of Palsberg and Zhao [17] .  ...  Palsberg and Zhao [17] presented an O(n 2 ) time algorithm for matching two recursive types. In this paper, we present an O(n log n) algorithm for the same problem.  ...  The final partition, where block {m 3 , m 4 , n 1 , n 2 } is split, is shown in the fourth row.  ... 
doi:10.1007/3-540-45931-6_14 fatcat:vfld3gvfivaatgokigp7riom2e

Efficient Type Matching [chapter]

Somesh Jha, Jens Palsberg, Tian Zhao, Fritz Henglein
2008 Automatic Program Development  
The O(n log n) algorithm for recursive types works by reducing the type matching problem to the problem of finding a size-stable partition of a graph, which has O(n log n) algorithms due to Cardon/Crochemore  ...  The key to these algorithms is the use of a "modify-the-smaller-half" approach pioneered by Hopcroft and Ullman for DFA minimization.  ...  Acknowledgments A preliminary version of the paper, authored by Jha, Palsberg, and Zhao, was presented at FOSSACS 2002. Palsberg was supported by an NSF CAREER award, CCR-9734265, and by IBM.  ... 
doi:10.1007/978-1-4020-6585-9_15 fatcat:4tf33j7wunabnakylbcveieokq

Metrics for Finite Markov Decision Processes [article]

Norman Ferns, Prakash Panangaden, Doina Precup
2012 arXiv   pre-print
The formulation of our metrics is based on the notion of bisimulation for MDPs, with an aim towards solving discounted infinite horizon reinforcement learning tasks.  ...  For future reference we will denote the iterates, F n © ¥ , by d n and remark that they form an ω-chain in M .  ...  Note that by induction d f ix R d n A c n T for every n. ¡ © A 7 S 4 log S lnδ lnc T operations.  ... 
arXiv:1207.4114v1 fatcat:la23i47tcfeorcvezzejutivpm

A Cure for Stuttering Parity Games [chapter]

Sjoerd Cranen, Jeroen J. A. Keiren, Tim A. C. Willemse
2012 Lecture Notes in Computer Science  
Governed stuttering bisimilarity can be decided in O(n 2 m) time for parity games with n vertices and m edges.  ...  We define governed stuttering bisimulation for parity games, weakening stuttering bisimulation by taking the ownership of vertices into account only when this might lead to observably different games.  ...  A ∼-minimal representation of a parity game (V, →, , P) is defined as a game (V m , → m , m , P m ), that satisfies the following conditions (where c, c , c ∈ V m ): V m = { [v]∼ | v ∈ V } m (c) =  ... 
doi:10.1007/978-3-642-32943-2_16 fatcat:y2qlvgv45jhedi5lgsxkogagaa

Tight Lower and Upper Bounds for the Complexity of Canonical Colour Refinement [article]

Christoph Berkholz, Paul Bonsma, Martin Grohe
2015 arXiv   pre-print
We give an O((m+n) n) algorithm for finding a canonical version of such a stable colouring, on graphs with n vertices and m edges.  ...  The goal of colour refinement is to find a stable colouring that uses a minimum number of colours.  ...  By Proposition 20, n ∈ O(2 k k) and m ∈ O(2 k k 2 ), so log n ∈ O(k). This shows that cost(α) ∈ ((m + n) log n).  ... 
arXiv:1509.08251v1 fatcat:yb4j4tzoivaa3cep7msj5qptge

Generic Partition Refinement and Weighted Tree Automata [article]

Hans-Peter Deifel, Stefan Milius, Lutz Schröder, Thorsten Wißmann
2019 arXiv   pre-print
Partition refinement is a method for minimizing automata and transition systems of various types.  ...  Genericity is achieved by modelling transition types as functors on sets, and systems as coalgebras.  ...  System Functor Run-Time Specific algorithm Transition Systems Pω m · log n = m · log n [20] Labelled TS Pω(N × −) m · log m = m · log m [10] > m · log n [26] Markov Chains R (−) m · log n = m · log n [  ... 
arXiv:1811.08850v3 fatcat:k5bpbbcjljde5fxehpnsodcmna

Tight Lower and Upper Bounds for the Complexity of Canonical Colour Refinement [chapter]

Christoph Berkholz, Paul Bonsma, Martin Grohe
2013 Lecture Notes in Computer Science  
We give an O((m + n) log n) algorithm for finding a canonical version of such a stable colouring, on graphs with n vertices and m edges.  ...  The goal of colour refinement is to find a stable colouring that uses a minimum number of colours.  ...  Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution  ... 
doi:10.1007/978-3-642-40450-4_13 fatcat:fbyky6w3ovh2ricvb2spmvenkq

From Generic Partition Refinement to Weighted Tree Automata Minimization [article]

Thorsten Wißmann, Hans-Peter Deifel, Stefan Milius, Lutz Schröder
2020 arXiv   pre-print
Partition refinement is a method for minimizing automata and transition systems of various types.  ...  Genericity is achieved by modelling transition types as functors on sets, and systems as coalgebras.  ...  −) · D ω m Dω · log m Pω < m · log n 2000 [BEM00] = m Dω · log m Pω 2018 [GVdV18] Colour Refinement B ω m · log n = m · log n 2017 [BBG17] Weighted Tree Automata M × M (Σ(−)) m · log 2 m < m · n 2007 [  ... 
arXiv:2004.01250v4 fatcat:4yooh6jlgjhinauj4gcvu7wtaq

Incremental Maintenance of the Minimum Bisimulation of Cyclic Graphs

Jintian Deng, Byron Choi, Jianliang Xu, Haibo Hu, Sourav S. Bhowmick
2013 IEEE Transactions on Knowledge and Data Engineering  
To the best of our knowledge, this is the first maintenance algorithm that guarantees minimum bisimulation of cyclic graphs.  ...  To study the problem with cyclic graphs, we first show that the two existing classes of minimization algorithms -merging algorithm and partition refinement -have their strengths and weaknesses.  ...  This work is supported by research grants GRFs HKBU210510 and HKBU210409, and FRG/07-08/I-59.  ... 
doi:10.1109/tkde.2012.230 fatcat:4asnbw34nnfyjbeslrdxbj6l7q

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George Barrett, Stéphane Lafortune
2012 Discrete event dynamic systems  
automaton with respect to the language of another automaton and a set of events in a worst-case running time of O(m log(n)), where m is the number of transitions and n is the number of states.  ...  , 1989) and bisimulation of automata models is derived.  ...  This research was supported in part by NSF grant ECS-9057967 and ARO grant DAAH04-96-1-0377. Notes  ... 
doi:10.1023/a:1008301317459 fatcat:vcpcaf2zrzdtlktsbcdifacuue

From generic partition refinement to weighted tree automata minimization

Thorsten Wißmann, Hans-Peter Deifel, Stefan Milius, Lutz Schröder
2021 Formal Aspects of Computing  
Genericity is achieved by modelling transition types as functors on sets, and systems as coalgebras.  ...  Moreover, the algorithm and the tool are modular, and partition refiners for new types of systems are obtained easily by composing pre-implemented basic functors.  ...  Simple P ω (A × −) · D ω m Dω · log m Pω < m · log n 2000 [BEM00] Segala Systems m Dω · log m Pω 2018 [GVdV18] Colour Refinement B ω m · log n m · log n 2017 [BBG17] Weighted Tree Automata M × M ( (−)  ... 
doi:10.1007/s00165-020-00526-z fatcat:fing7b2ibvcxhfpxs2nkutr2uy

Efficient Solution of Optimal Control Problems Using Hybrid Systems

Mireille Broucke, Maria Domenica Di Benedetto, Stefano Di Gennaro, Alberto Sangiovanni-Vincentelli
2005 SIAM Journal of Control and Optimization  
An algorithmic solution is obtained by translating the hybrid automaton to a finite automaton using a bisimulation and formulating a dynamic programming problem with extra conditions to ensure non-Zenoness  ...  locations in which the control is constant.  ...  We obtain a partition of the domain provided by a bisimulation partition.  ... 
doi:10.1137/s0363012900383090 fatcat:q6xrnv7txve5plo64vw4t3acci

The Complexity of Bisimulation and Simulation on Finite Systems [article]

Moses Ganardi, Stefan Göller, Markus Lohrey
2018 arXiv   pre-print
Furthermore, if only one of the input graphs is required to be a tree, the bisimulation (simulation) problem is contained in AC^1 (LogCFL).  ...  In contrast, it is also shown that the simulation problem is P-complete already for graphs of bounded path-width.  ...  By [GLS01, Lemma 4.6] we can assume that C is layered and alternating, i.e., the set of gates is partitioned into m ∈ O(log n) many layers L 1 , L 2 , . . . , L m , where m > 1 is odd, L 1 contains the  ... 
arXiv:1806.00256v1 fatcat:3qmsuonnurb2jpystyfioqtlli
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