On labeled birooted tree languages: Algebras, automata and logic

Janin, David

doi:10.1016/j.ic.2014.12.016

Cited by 6 publications

(3 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It has already been observed that an adequate algebraic theory for inverse monoid morphisms can be developed by means of certain kind of premorphisms instead of morphisms [9,10,12,14]. As a matter of fact, transition monoids of walking automata induce a different type of premorphisms that could also be investigated as new language recognizers.…”

Section: Resultsmentioning

confidence: 99%

“…Taking the group defined from A = {a, b, c, d} by cc = 1, dd = 1 and cd = 0, we obtain vertex-labeled birooted trees with edges labeled by a or b and, following Remark 5, vertices labeled over P({c, d}). Thanks to the axiom cd = 0, only the birooted graph encoding zero has a vertex labeled by both c and d. The language theory of these vertex-labeled birooted graphs has been studied in [10,14].…”

Section: Remark 18mentioning

confidence: 99%

See 1 more Smart Citation

Walking Automata in Free Inverse Monoids

Janin

2016

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Walking automata, be they running over words, trees or even graphs, possibly extended with pebbles that can be dropped and lifted on vertices, have long been defined and studied in Computer Science. However, questions concerning walking automata are surprisingly complex to solve. In this paper, we study a generic notion of walking automata over graphs whose semantics naturally lays within inverse semigroup theory. Then, from the simplest notion of walking automata on birooted trees, that is, elements of free inverse monoids, to the more general cases of walking automata on birooted finite subgraphs of Cayley's graphs of groups, that is, elements of free E-unitary inverse monoids, we provide a robust algebraic framework in which various classes of recognizable or regular languages of birooted graphs can uniformly be defined and related one with the other. 1 Introduction General context. Walking automata, be they running over words, trees or even graphs, possibly extended with pebbles, have long been defined and studied in Computer Science[7,8]. For instance, tree walking automata with pebbles have been an important subject of study the last decades since they are natural abstract models of machine for XML query languages such as XPATH, or XML transformation languages such as XSL [6]. Although based on well studied computation models: finite state machines or pushdown automata, questions about walking automata are often surprisingly complex to solve and, to a lesser extent, quite dependent on such or such details in automata's definition. For instance, in the case of tree languages, bounding the number of pebbles an automaton leads to defining classes of recognizable languages. Various logical characterizations of these classes have been obtained [8] and difficult separation results have also been proved [2,3,1]. However, for separation results, proof arguments apply to the case of pebbles that are marked and visible [2,3], leaving open the cases of unmarked and/or invisible pebbles. Even though walking automata are sequential machines much like string automata, the classical algebraic tools that have been developed to study word automata are not easily applicable to tree walking automata. Despite numerous results, little is known about the underlying mathematical framework, say in algebra, that walking automata may induce. Contribution of the paper. In this paper, we initiate the development of an algebraic framework, within inverse semigroup theory, for walking automata. We provide a generic notion of automata walking on edge-labeled graphs. They act as some kind of observers of their input graphs much in the same way observational semantics has been defined in concurrency theory by Hennessy and Milner [17]. Unlike most classical definitions, we do not require walking automata to start and end in the same vertex, neither do we require the complete traversal of input structures. Moreover, the capacity given to a walking automaton to check or not the absence of an (incoming or outgoing) edge labeled by a given lett...

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Remark 18mentioning

confidence: 99%

Walking Automata in Free Inverse Monoids

Janin

2016

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…Although not much popular even in theoretical computer science, it is known that their free algebras capture deterministic unranked trees [13]. They have recently been studied in formal language theory by the second author for developing a new algebraic characterization of regular languages of finite trees [11]. It is conjectured that dropping the commutation hypothesis (property (8)) will eventually lead to languages of ranked trees.…”

Section: Related Workmentioning

confidence: 99%

Unified media programming: an algebraic approach

Archipoff

Janin

2017

Proceedings of the 5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design

Self Cite

View full text Add to dashboard Cite

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Public Domain

show abstract

Language acceptability of finite automata based on theory of semi‐tensor product of matrices

Yue

Yan

Chen

2019

Asian Journal of Control

View full text Add to dashboard Cite

Using the theories of many‐valued logic and semi‐tensor product of matrices (STP), this paper investigates how to mathematically determine whether or not a regular language is recognized by finite automata (FA). To this end, the dynamic behaviour of FA is first formulated as bilinear dynamic equations, which provides a uniform model for deterministic and non‐deterministic FA. Based on the bilinear model, the recognition power of FA understanding of regular languages is investigated and several algebraic criteria are obtained. With the algebraic criteria, to judge whether a regular sentence is accepted by a FA or not, one only needs to calculate an STP of some vectors, rather than making the sentence run over the machine as traditional manners. Further, the inverse problem of recognition is considered, an algorithm is developed that can mathematically construct all the accepted sentences for a given FA. The algebraic approach of this paper may be a new angle and means to understand and analyse the dynamics of FA.

show abstract

On labeled birooted tree languages: Algebras, automata and logic

Cited by 6 publications

References 50 publications

Walking Automata in Free Inverse Monoids

Walking Automata in Free Inverse Monoids

Unified media programming: an algebraic approach

Language acceptability of finite automata based on theory of semi‐tensor product of matrices

Contact Info

Product

Resources

About