Simulations of Weighted Tree Automata

Ésik, Zoltán; Maletti, Andreas

doi:10.1007/978-3-642-18098-9_34

Cited by 5 publications

(5 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, following and [6,13], we introduce simulations between descriptions, and show that descriptions that can be connected by a sequence of simulations are equivalent. Let K denote a commutative semiring.…”

Section: Simulationsmentioning

confidence: 99%

“…. In [13], it is shown that all commutative rings are proper. More generally, let us call a (commutative) semiring Noetherian, if for every finitely generated K-semimodule M , every subsemimodule of M is finitely generated.…”

Section: Simulationsmentioning

confidence: 99%

“…More generally, let us call a (commutative) semiring Noetherian, if for every finitely generated K-semimodule M , every subsemimodule of M is finitely generated. It is shown in [13] that if K is Noetherian, or every finitely generated subsemiring of K is contained in a Noetherian subsemiring, then K is proper. In particular, every locally finite 1 (commutative) semiring and thus every bounded distributive lattice is proper.…”

Section: Simulationsmentioning

confidence: 99%

“…There exist proper semirings that are not Noetherian, for example the semiring N, cf. [3,13]. An example of a semiring that is not proper is the "tropical semiring", cf.…”

Section: Simulationsmentioning

confidence: 99%

See 3 more Smart Citations

Multi-Linear Iterative K-Σ-Semialgebras

ísik

2011

Electronic Notes in Theoretical Computer Science

View full text Add to dashboard Cite

We consider K-semialgebras for a commutative semiring K that are at the same time Σ-algebras and satisfy certain linearity conditions. When each finite system of guarded polynomial fixed point equations has a unique solution over such an algebra, then we call it an iterative multi-linear K-Σ-semialgebra. Examples of such algebras include the algebras of Σ-tree series over an alphabet A with coefficients in K, and the algebra of all rational tree series. We show that for many commutative semirings K, the rational Σ-tree series over A with coefficients in K form the free multi-linear iterative K-Σ-semialgebra on A.Definition 2.1 Suppose that X is a set of variables and A is an alphabet of parameters. We call a term t over X in the parameters A proper (or guarded), if it is either 0, or a letter a in A, or a term of the form σ(t 1 , . . . , t n ), σ ∈ Σ n , n ≥ 0, where t 1 , . . . , t n are any terms over X in the parameters A, or a term of the form kt or t 1 + t 2 , where t, t 1 , t 2 are proper terms and k ∈ K.Since for any term t, the term 0t can be identified with 0, we could as well allow proper terms of the form 0t, where t is any term.

show abstract

Section: Simulationsmentioning

confidence: 99%

Section: Simulationsmentioning

confidence: 99%

Section: Simulationsmentioning

confidence: 99%

“…There exist proper semirings that are not Noetherian, for example the semiring N, cf. [3,13]. An example of a semiring that is not proper is the "tropical semiring", cf.…”

Section: Simulationsmentioning

confidence: 99%

See 2 more Smart Citations

Multi-Linear Iterative K-Σ-Semialgebras

ísik

2011

Electronic Notes in Theoretical Computer Science

View full text Add to dashboard Cite

show abstract

“…Definition 2.1 ( [ Ésik and Maletti 2011]). A semiring S is called Noetherian if every subsemimodule of a finitely generated S-semimodule is itself finitely generated.…”

Section: S-modmentioning

confidence: 99%

Sound and complete axiomatizations of coalgebraic language equivalence

Bonsangue,

Milius,

Silva

2011

Preprint

View full text Add to dashboard Cite

Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are sound and complete with respect to behavioral equivalence can be extended to a coarser coalgebraic language equivalence, which arises from a generalised powerset construction that determinises coalgebras. We show that soundness and completeness are established by proving that expressions modulo axioms of a calculus form the rational fixpoint of the given type functor. Our main result is that the rational fixpoint of the functor F T , where T is a monad describing the branching of the systems (e.g. nondeterminism, weights, probability etc.), has as a quotient the rational fixpoint of the "determinised" type functor F , a lifting of F to the category of T -algebras. We apply our framework to the concrete example of weighted automata, for which we present a new sound and complete calculus for weighted language equivalence. As a special case, we obtain non-deterministic automata, where we recover Rabinovich's sound and complete calculus for language equivalence.

show abstract