scholarly journals FINITE TREE AUTOMATA ON INFINITE TREES

10.5109/13369 ◽  
1985 ◽  
Vol 21 (3/4) ◽  
pp. 71-82 ◽  
Author(s):  
Takeshi Hayashi ◽  
Satoru Miyano
Keyword(s):  
Tree Automata ◽  
Finite Tree ◽  
Infinite Trees

Deciding Equivalence of Finite Tree Automata

1990 ◽  
Vol 19 (3) ◽  
pp. 424-437 ◽  
Author(s):  
Helmut Seidl
Keyword(s):  
Tree Automata ◽  
Finite Tree

scholarly journals A Congruence-Based Perspective on Finite Tree Automata

2022 ◽  
Vol 184 (1) ◽  
pp. 1-47
Author(s):  
Pierre Ganty ◽  
Elena Gutiérrez ◽  
Pedro Valero
Keyword(s):  
Expressive Power ◽  
Tree Automata ◽  
Minimization Algorithm ◽  
Top Down ◽  
Finite Tree ◽  
Bottom Up ◽  
Original Result

We provide new insights on the determinization and minimization of tree automata using congruences on trees. From this perspective, we study a Brzozowski’s style minimization algorithm for tree automata. First, we prove correct this method relying on the following fact: when the automata-based and the language-based congruences coincide, determinizing the automaton yields the minimal one. Such automata-based congruences, in the case of word automata, are defined using pre and post operators. Now we extend these operators to tree automata, a task that is particularly challenging due to the reduced expressive power of deterministic top-down (or equivalently co-deterministic bottom-up) automata. We leverage further our framework to offer an extension of the original result by Brzozowski for word automata.

scholarly journals Monoidal-closed categories of tree automata

2020 ◽  
Vol 30 (1) ◽  
pp. 62-117
Author(s):  
Colin Riba
Keyword(s):  
Linear Logic ◽  
Tree Automata ◽  
Sequential Games ◽  
Infinite Trees ◽  
Alternating Tree Automata ◽  
Deduction Rules ◽  
New Perspective ◽  
Alternating Automata ◽  
Second Order Logic ◽  
Monadic Second Order Logic

AbstractThis paper surveys a new perspective on tree automata and Monadic second-order logic (MSO) on infinite trees. We show that the operations on tree automata used in the translations of MSO-formulae to automata underlying Rabin’s Tree Theorem (the decidability of MSO) correspond to the connectives of Intuitionistic Multiplicative Exponential Linear Logic (IMELL). Namely, we equip a variant of usual alternating tree automata (that we call uniform tree automata) with a fibered monoidal-closed structure which in particular handles a linear complementation of alternating automata. Moreover, this monoidal structure is actually Cartesian on non-deterministic automata, and an adaptation of a usual construction for the simulation of alternating automata by non-deterministic ones satisfies the deduction rules of the !(–) exponential modality of IMELL. (But this operation is unfortunately not a functor because it does not preserve composition.) Our model of IMLL consists in categories of games which are based on usual categories of two-player linear sequential games called simple games, and which generalize usual acceptance games of tree automata. This model provides a realizability semantics, along the lines of Curry–Howard proofs-as-programs correspondence, of a linear constructive deduction system for tree automata. This realizability semantics, which can be summarized with the slogan “automata as objects, strategies as morphisms,” satisfies an expected property of witness extraction from proofs of existential statements. Moreover, it makes it possible to combine realizers produced as interpretations of proofs with strategies witnessing (non-)emptiness of tree automata.

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