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Lowerbounds for Bisimulation by Partition Refinement
[article]
2022
arXiv
pre-print
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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 Ω((m+n) log n). ...
arXiv:2203.07158v1
fatcat:ctwvc2yanjelta6q7elyarf6vq
A Fast Bisimulation Algorithm
[chapter]
2001
Lecture Notes in Computer Science
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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]
2002
Lecture Notes in Computer Science
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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]
2008
Automatic Program Development
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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]
2012
arXiv
pre-print
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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]
2012
Lecture Notes in Computer Science
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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, →, Ω, P) is defined as a game (V m , → m , Ω m , P m ), that satisfies the following conditions (where c, c , c ∈ V m ): V m = { [v]∼ | v ∈ V } Ω 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]
2015
arXiv
pre-print
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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) ∈ Ω((m + n) log n). ...
arXiv:1509.08251v1
fatcat:yb4j4tzoivaa3cep7msj5qptge
Generic Partition Refinement and Weighted Tree Automata
[article]
2019
arXiv
pre-print
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2019 pre-print arXiv:1811.08850v2 fatcat:3k5dhn3pmvfdzj4zafv5w3mpw4Other Versions
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]
2013
Lecture Notes in Computer Science
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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]
2020
arXiv
pre-print
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2020 pre-print arXiv:2004.01250v2 fatcat:uz62a3gw5reydfdqbrdrswhgomOther Versions
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
2013
IEEE Transactions on Knowledge and Data Engineering
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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
:{unav)
2012
Discrete event dynamic systems
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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
2021
Formal Aspects of Computing
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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
2005
SIAM Journal of Control and Optimization
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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]
2018
arXiv
pre-print
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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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