Bisimulation Minimisation for Weighted Tree Automata

Högberg, Johanna; Maletti, Andreas; May, Jonathan

doi:10.1007/978-3-540-73208-2_23

Cited by 16 publications

(41 citation statements)

References 18 publications

(26 reference statements)

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“…Reduction of automata from some of such classes has already been considered in the literature (e.g., in [8], the author proposes a bisimulation-based minimisation of weighted word automata, and a use of bisimulations for reducing weighted tree automata is considered in [10]). …”

Section: Discussionmentioning

confidence: 99%

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A Uniform (Bi-)Simulation-Based Framework for Reducing Tree Automata

Abdulla

Holík

Kaati

et al. 2009

Electronic Notes in Theoretical Computer Science

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In this paper, we address the problem of reducing the size of nondeterministic (bottom-up) tree automata. We propose a uniform framework that allows for combining various upward and downward bisimulation and simulation relations in order to obtain a language-preserving combined relation suitable for reducing tree automata without a need to determinise them. The framework generalises and extends several previous works and provides a broad spectrum of different relations yielding a possibility of a fine choice between the amount of reduction and the computational demands. We, moreover, provide a significantly improved way of computing the various combined (bi-)simulation relations. We analyse properties of the considered relations both theoretically as well as through a series of experiments.

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Section: Discussionmentioning

confidence: 99%

“…We prove this claim by the following counterexample. 10 and F = Q. Let us choose the relation R = id ∪ {(q, r), (r, t), (q, t)}, which is apparently contained in LP , as the inducing preorder.…”

Section: Impossibility Of Relaxing the Need Of Downward Simulationsmentioning

confidence: 99%

A Uniform (Bi-)Simulation-Based Framework for Reducing Tree Automata

Abdulla

Holík

Kaati

et al. 2009

Electronic Notes in Theoretical Computer Science

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“…The bijection will be established by evaluating the access trees in N. Formally, we let h: Q → P be such that h(q) = μ(t q ) for every q ∈ Q , which immediately proves that h(q) ∈ Ker(N) for all q ∈ Ker(M) because ht(t q ) > |Q × P |. Moreover, for each q ∈ Ker(M) the facts M ∼ N and 9 Finally, for every p ∈ Ker(N), select u p ∈ L(N) p such that ht(u p ) > |Q × P |. Clearly, δ(u p ) ∈ Ker(M) and by Lemma 3 we obtain…”

Section: Theorem 6 If M ∼ N and Both M And N Are Hyper-minimal Thenmentioning

confidence: 98%

“…Classical examples in the area of natural language processing include the estimation of probabilistic tree automata [1][2][3] for parsing [4], probabilistic finite-state automata [5] for speech recognition [6], and probabilistic finite-state transducers [7] for machine translation [8]. Since those models tend to become huge, various efficient minimization techniques (such as the merge-steps in the Berkeley parser training [4] or bisimulation minimization [9,10]) are used. Unfortunately, already the computation of an equivalent minimal nondeterministic finite-state automaton (NFA) [11] given an input NFA is PSPACE-complete [12] and thus inefficient; this remains true even if the input NFA is deterministic.…”

Section: Introductionmentioning

confidence: 99%

Hyper-optimization for deterministic tree automata

Maletti

2015

Theoretical Computer Science

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DTA = deterministic tree automaton DBA / DCA = deterministic BÜCHI / Co-BÜCHI automaton Deterministic Tree Automaton Definition (GÉCSEG, STEINBY 1984) (Q, Σ, δ, F ) deterministic tree automaton (DTA) Q finite set states Σ ranked alphabet input symbolsDeterministic Tree Automaton Definition (GÉCSEG, STEINBY 1984) (Q, Σ, δ, F ) deterministic tree automaton (DTA) Q finite set states Σ ranked alphabet input symbolsDeterministic Tree Automaton Example states q α , q β (nonfinal) and q γ , q σ (final) nullary input symbols α, β, γ and binary σ for all nullary symbols π, πDeterministic Tree Automaton Example states q α , q β (nonfinal) and q γ , q σ (final) nullary input symbols α, β, γ and binary σ for all nullary symbols π, πDeterministic Tree Automaton Example states q α , q β (nonfinal) and q γ , q σ (final) nullary input symbols α, β, γ and binary σ for all nullary symbols π, πDeterministic Tree Automaton Example states q α , q β (nonfinal) and q γ , q σ (final) nullary input symbols α, β, γ and binary σ for all nullary symbols π, πDeterministic Tree Automaton Example states q α , q β (nonfinal) and q γ , q σ (final) nullary input symbols α, β, γ and binary σ for all nullary symbols π, πDeterministic Tree Automaton Example states q α , q β (nonfinal) and q γ , q σ (final) nullary input symbols α, β, γ and binary σ for all nullary symbols π, πDeterministic Tree Automaton Definition (Recognized tree language)

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“…8 runs in time OðM 2 N 3 Þ for a directed graph with N vertices and M edges. If the network has labels on the edges, complexity is increased by a factor as large as the size of the number of different labels.If the network has integers as weights (and we assume that comparisons can be done in constant time) the time complexity remains the same (Högberg et al 2007). …”

Section: Algorithmmentioning

confidence: 99%

Social positions and simulation relations

Brynielsson

Kaati

Svenson

2011

Soc. Netw. Anal. Min.

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Describing social positions and roles is an important topic within the social network analysis. Identifying social positions can be difficult when the target organization lacks a formal structure or is partially hidden. One approach is to compute a suitable equivalence relation on the nodes of the target network. Several different equivalence relations can be used, all depending on what kind of social positions that are of interest.One relation that is often used for this purpose is regular equivalence, or bisimulation, as it is known within the field of computer science. In this paper we consider a relation from computer science called simulation relation. The simulation relation creates a partial order on the set of actors in a network and we can use this order to identify actors that have characteristic properties. The simulation relation can also be used to compute simulation equivalence which is a related but less restrictive equivalence relation than regular equivalence that is still computable in polynomial time.We tentatively term the equivalence classes determined by simulation equivalence social positions. Which equivalence relation that is interesting to consider depends on the problem at hand. We argue that it is necessary to consider several different equivalence relations for a given network, in order to understand it completely. This paper primarily considers weighted directed networks and we present definitions of both weighted simulation equivalence and weighted regular equivalence. Weighted networks can be used to model a number of network domains, including information flow, trust propagation, and communication channels. Many of these domains have applications within homeland security and in the military, where one wants to survey and elicit key roles within an organization. After social positions have been calculated, they can be used to produce abstractions of the network-smaller versions that retain some of the most important characteristics.

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Bisimulation Minimisation for Weighted Tree Automata

Cited by 16 publications

References 18 publications

A Uniform (Bi-)Simulation-Based Framework for Reducing Tree Automata

A Uniform (Bi-)Simulation-Based Framework for Reducing Tree Automata

Hyper-optimization for deterministic tree automata

Social positions and simulation relations

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