Congruence-based proofs of the recognizability theorems for free many-sorted algebras

2020 ◽  
Vol 30 (2) ◽  
pp. 561-633
Author(s):  
J Climent Vidal ◽  
E Cosme LlÓpez
Keyword(s):  
Tree Automata ◽  
Regular Tree ◽  
Algebraic Proofs

Abstract We generalize several recognizability theorems for free single-sorted algebras to free many-sorted algebras and provide, in a uniform way and without using either regular tree grammars or tree automata, purely algebraic proofs of them based on congruences.

scholarly journals A generic parser for strings and trees

2012 ◽  
Vol 9 (1) ◽  
pp. 381-410
Author(s):  
Riad Jabri
Keyword(s):  
Pattern Matching ◽  
Code Generation ◽  
Tree Automata ◽  
Extended Version ◽  
Context Free Grammar ◽  
Regular Tree ◽  
Direct Mapping ◽  
Parsing Algorithm ◽  
Input Strings ◽  
Context Free

In this paper, we propose a two fold generic parser. First, it simulates the behavior of multiple parsing automata. Second, it parses strings drawn from either a context free grammar, a regular tree grammar, or from both. The proposed parser is based on an approach that defines an extended version of an automaton, called positionparsing automaton (PPA) using concepts from LR and regular tree automata, combined with a newly introduced concept, called state instantiation and transition cloning. It is constructed as a direct mapping from a grammar, represented in an expanded list format. However, PPA is a non-deterministic automaton with a generic bottom-up parsing behavior. Hence, it is efficiently transformed into a reduced one (RBA). The proposed parser is then constructed to simulate the run of the RBA automaton on input strings derived from a respective grammar. Without loss of generality, the proposed parser is used within the framework of pattern matching and code generation. Comparisons with similar and well-known approaches, such as LR and RI, have shown that our parsing algorithm is conceptually simpler and requires less space and states.

The Bottom-Up Position Tree Automaton and the Father Automaton

2020 ◽  
pp. 1-18
Author(s):  
Samira Attou ◽  
Ludovic Mignot ◽  
Djelloul Ziadi
Keyword(s):  
Tree Automaton ◽  
Tree Automata ◽  
Top Down ◽  
Bottom Up ◽  
Regular Tree ◽  
The One ◽  
Tree Expression

The conversion of a given regular tree expression into a tree automaton has been widely studied. However, classical interpretations are based upon a top-down interpretation of tree automata. In this paper, we propose new constructions based on Gluskov’s one and on the one by Ilie and Yu using a bottom-up interpretation. One of the main goals of this technique is to consider as a next step the links with deterministic recognizers, something which cannot be done with classical top-down approaches.

Projection for Büchi Tree Automata with Constraints between Siblings

2020 ◽  
Vol 31 (06) ◽  
pp. 749-775
Author(s):  
Patrick Landwehr ◽  
Christof Löding
Keyword(s):  
Decision Procedure ◽  
Order Logic ◽  
Tree Automata ◽  
Boolean Operations ◽  
Regular Tree ◽  
Infinite Trees ◽  
Acceptance Condition ◽  
Emptiness Problem ◽  
Second Order Logic ◽  
Monadic Second Order Logic

We consider an extension of tree automata on infinite trees that can use equality and disequality constraints between direct subtrees of a node. Recently, it has been shown that the emptiness problem for these kind of automata with a parity acceptance condition is decidable and that the corresponding class of languages is closed under Boolean operations. In this paper, we show that the class of languages recognizable by such tree automata with a Büchi acceptance condition is closed under projection. This construction yields a new algorithm for the emptiness problem, implies that a regular tree is accepted if the language is non-empty (for the Büchi condition), and can be used to obtain a decision procedure for an extension of monadic second-order logic with predicates for subtree comparisons.

Multiple Regularity and Binary ETOL-Systems1

1981 ◽  
Vol 4 (1) ◽  
pp. 19-34
Author(s):  
Ryszard Danecki
Keyword(s):  
Equivalence Problem ◽  
Tree Automata ◽  
Closure Properties ◽  
Multiple Tree

Closure properties of binary ETOL-languages are investigated by means of multiple tree automata. Decidability of the equivalence problem of deterministic binary ETOL-systems is proved.

Sign in / Sign up

Export Citation Format

Share Document