Generalizing determinization from automata to coalgebras

Silva, Alexandra; Bonchi, Filippo; Bonsangue, Marcello M.; Rütten, Jan

doi:10.2168/lmcs-9(1:9)2013

Cited by 58 publications

(83 citation statements)

References 46 publications

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“…By instantiating the operational analysis of computational effects from [24] to our setting we arrive at syntactic fixpoint expressions representing T-automata and prove a Kleenestyle theorem for them, thus generalizing previous work of the third author [34]. A crucial ingredient of our framework is the generalized powerset construction [35], which serves as a coalgebraic counterpart of classical Rabin-Scott determinization algorithm [26]. It allows us to define trace semantics of T-automata and fixpoint expressions denoting their behavior.…”

Section: Introductionmentioning

confidence: 95%

“…In order to deal with other levels we introduce (finitary) monads and algebraic theories as a critical ingredient of our formalization, thus building on top of the recent previous work [15,35]. One way to give a monad is by giving a Kleisli triple.…”

Section: Monads and Algebraic Theoriesmentioning

confidence: 99%

“…This conversion is called the generalized powerset construction [26] as it generalizes the classical Rabin and Scott NFSM determinization [35]. Observe that LT X is a Talgebra, since T X is the free T-algebra on X and L lifts to Set T (see Remark 4.2).…”

Section: Reactive T-algebras and T-automatamentioning

confidence: 99%

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Towards a Coalgebraic Chomsky Hierarchy

Goncharov¹,

Milius²,

Silva³

2014

Lecture Notes in Computer Science

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Abstract. The Chomsky hierarchy plays a prominent role in the foundations of theoretical computer science relating classes of formal languages of primary importance. In this paper we use recent developments on coalgebraic and monadbased semantics to obtain a generic notion of a T-automaton, where T is a monad, which allows the uniform study of various notions of machines (e.g. finite state machines, multi-stack machines, Turing machines, valence automata, weighted automata). We use the generalized powerset construction to define a generic (trace) semantics for T-automata, and we show by numerous examples that it correctly instantiates for some known classes of machines/languages captured by the Chomsky hierarchy. Moreover, our approach provides new generic techniques for studying expressivity power of various machine-based models.

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Section: Introductionmentioning

confidence: 95%

Section: Monads and Algebraic Theoriesmentioning

confidence: 99%

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Towards a Coalgebraic Chomsky Hierarchy

Goncharov¹,

Milius²,

Silva³

2014

Lecture Notes in Computer Science

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“…A -coalgebras, but they can be embedded into one, using some kind of determinization procedure (as introduced in [12]). …”

Section: Introductionmentioning

confidence: 99%

“…[8,9,1]. Our construction in Section 3 can be seen as an instance of the generalized determinization construction described in [12]. Finally, our work relies largely on coinductive calculus for streams and power series, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Coalgebraic Semantics of Heavy-Weighted Automata

Fortin

Bonsangue

Rütten

2015

Recent Trends in Algebraic Development Techniques

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Abstract. In this paper we study heavy-weighted automata, a generalization of weighted automata in which the weights of the transitions can be formal power series. As for ordinary weighted automata, the behaviour of heavy-weighted automata is expressed in terms of formal power series. We propose several equivalent definitions for their semantics, including a system of behavioural differential equations (following the approach of coinductive calculus), or an embedding into a coalgebra for the functor S × (−)A , for which the set of formal power series is a final coalgebra. Using techniques based on bisimulations and coinductive calculus, we study how ordinary weighted automata can be transformed into more compact heavy-weighted ones.

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Long-Term Values in Markov Decision Processes, (Co)Algebraically

Feys

Hansen

Moss

2018

Coalgebraic Methods in Computer Science

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This paper studies Markov decision processes (MDPs) from the categorical perspective of coalgebra and algebra. Probabilistic systems, similar to MDPs but without rewards, have been extensively studied, also coalgebraically, from the perspective of program semantics. In this paper, we focus on the role of MDPs as models in optimal planning, where the reward structure is central. The main contributions of this paper are (i) to give a coinductive explanation of policy improvement using a new proof principle, based on Banach's Fixpoint Theorem, that we call contraction coinduction, and (ii) to show that the long-term value function of a policy with respect to discounted sums can be obtained via a generalized notion of corecursive algebra, which is designed to take boundedness into account. We also explore boundedness features of the Kantorovich lifting of the distribution monad to metric spaces.

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Generalizing determinization from automata to coalgebras

Cited by 58 publications

References 46 publications

Towards a Coalgebraic Chomsky Hierarchy

Towards a Coalgebraic Chomsky Hierarchy

Coalgebraic Semantics of Heavy-Weighted Automata

Long-Term Values in Markov Decision Processes, (Co)Algebraically

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