A (co)algebraic theory of succinct automata

Gerco van Heerdt; Joshua Moerman; Matteo Sammartino; Alexandra Silva

doi:10.1016/j.jlamp.2019.02.008

A (co)algebraic theory of succinct automata

Gerco van Heerdt, Joshua Moerman, Matteo Sammartino, Alexandra Silva

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

The classical subset construction for non-deterministic automata can be generalized to other side-effects captured by a monad. The key insight is that both the state space of the determinized automaton and its semantics—languages over an alphabet—have a common algebraic structure: they are Eilenberg-Moore algebras for the powersetgen monad. In this paper we study the reverse question to determinization. We will present a construction to associate succinct automata to languages based on different algebraic structures. For instance, for classical regular languages the construction will transform a deterministic automaton into a non-deterministic one, where the states represent the join-irreducibles of the language accepted by a (potentially) larger deterministic automaton. Other examples will yield alternating automata, automata with symmetries, CABA-structured automata, and weighted automata.

Original language	English
Pages (from-to)	112-125
Number of pages	14
Journal	Journal of Logical and Algebraic Methods in Programming
Volume	105
DOIs	https://doi.org/10.1016/j.jlamp.2019.02.008
Publication status	Published - Jun 2019
Externally published	Yes

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title = "A (co)algebraic theory of succinct automata",

abstract = "The classical subset construction for non-deterministic automata can be generalized to other side-effects captured by a monad. The key insight is that both the state space of the determinized automaton and its semantics—languages over an alphabet—have a common algebraic structure: they are Eilenberg-Moore algebras for the powersetgen monad. In this paper we study the reverse question to determinization. We will present a construction to associate succinct automata to languages based on different algebraic structures. For instance, for classical regular languages the construction will transform a deterministic automaton into a non-deterministic one, where the states represent the join-irreducibles of the language accepted by a (potentially) larger deterministic automaton. Other examples will yield alternating automata, automata with symmetries, CABA-structured automata, and weighted automata.",

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doi = "10.1016/j.jlamp.2019.02.008",

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AU - Moerman, Joshua

AU - Sammartino, Matteo

AU - Silva, Alexandra

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PY - 2019/6

Y1 - 2019/6

N2 - The classical subset construction for non-deterministic automata can be generalized to other side-effects captured by a monad. The key insight is that both the state space of the determinized automaton and its semantics—languages over an alphabet—have a common algebraic structure: they are Eilenberg-Moore algebras for the powersetgen monad. In this paper we study the reverse question to determinization. We will present a construction to associate succinct automata to languages based on different algebraic structures. For instance, for classical regular languages the construction will transform a deterministic automaton into a non-deterministic one, where the states represent the join-irreducibles of the language accepted by a (potentially) larger deterministic automaton. Other examples will yield alternating automata, automata with symmetries, CABA-structured automata, and weighted automata.

AB - The classical subset construction for non-deterministic automata can be generalized to other side-effects captured by a monad. The key insight is that both the state space of the determinized automaton and its semantics—languages over an alphabet—have a common algebraic structure: they are Eilenberg-Moore algebras for the powersetgen monad. In this paper we study the reverse question to determinization. We will present a construction to associate succinct automata to languages based on different algebraic structures. For instance, for classical regular languages the construction will transform a deterministic automaton into a non-deterministic one, where the states represent the join-irreducibles of the language accepted by a (potentially) larger deterministic automaton. Other examples will yield alternating automata, automata with symmetries, CABA-structured automata, and weighted automata.

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JO - Journal of Logical and Algebraic Methods in Programming

JF - Journal of Logical and Algebraic Methods in Programming

ER -

A (co)algebraic theory of succinct automata

Abstract

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