139 research outputs found
Simulations of Weighted Tree Automata
Simulations of weighted tree automata (wta) are considered. It is shown how
such simulations can be decomposed into simpler functional and dual functional
simulations also called forward and backward simulations. In addition, it is
shown in several cases (fields, commutative rings, Noetherian semirings,
semiring of natural numbers) that all equivalent wta M and N can be joined by a
finite chain of simulations. More precisely, in all mentioned cases there
exists a single wta that simulates both M and N. Those results immediately
yield decidability of equivalence provided that the semiring is finitely (and
effectively) presented.Comment: 17 pages, 2 figure
Scattered one-counter languges have rank less than
A linear ordering is called context-free if it is the lexicographic ordering
of some context-free language and is called scattered if it has no dense
subordering. Each scattered ordering has an associated ordinal, called its
rank. It is known that scattered context-free (regular, resp.) orderings have
rank less than (, resp).
In this paper we confirm the conjecture that one-counter languages have rank
less than
A String Diagrammatic Axiomatisation of Finite-State Automata
We develop a fully diagrammatic approach to the theory of finite-state
automata, based on reinterpreting their usual state-transition graphical
representation as a two-dimensional syntax of string diagrams. Moreover, we
provide an equational theory that completely axiomatises language equivalence
in this new setting. This theory has two notable features. First, the Kleene
star is a derived concept, as it can be decomposed into more primitive
algebraic blocks. Second, the proposed axiomatisation is finitary -- a result
which is provably impossible to obtain for the one-dimensional syntax of
regular expressions.Comment: Minor corrections, in particular in the proof of completeness
(including the ordering of the steps of Brzozowski's algorithm
On the Order Type of Scattered Context-Free Orderings
We show that if a context-free grammar generates a language whose
lexicographic ordering is well-ordered of type less than , then its
order type is effectively computable.Comment: In Proceedings GandALF 2019, arXiv:1909.05979. arXiv admin note: text
overlap with arXiv:1907.1157
Reversible Kleene lattices
International audienceWe investigate the equational theory of reversible Kleene lattices, that is algebras of languages with the regular operations (union, composition and Kleene star), together with the intersection and mirror image. Building on results by Andréka, Mikulás and Németi from 2011, we construct the free representation of this algebra. We then provide an automaton model to compare representations. These automata are adapted from Petri automata, which we introduced with Pous in 2015 to tackle a similar problem for algebras of binary relations. This allows us to show that testing the validity of equations in this algebra is decidable, and in fact ExpSpace-complete
A FINITE AXIOMATISATION OF FINITE-STATE AUTOMATA USING STRING DIAGRAMS
We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a complete equational theory for language equivalence, with two notable features. First, the proposed axiomatisation is finite. Second, the Kleene star is a derived concept, as it can be decomposed into more primitive algebraic blocks
A Finite Axiomatisation of Finite-State Automata Using String Diagrams
We develop a fully diagrammatic approach to finite-state automata, based on
reinterpreting their usual state-transition graphical representation as a
two-dimensional syntax of string diagrams. In this setting, we are able to
provide a complete equational theory for language equivalence, with two notable
features. First, the proposed axiomatisation is finite. Second, the Kleene star
is a derived concept, as it can be decomposed into more primitive algebraic
blocks.Comment: arXiv admin note: text overlap with arXiv:2009.1457
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