Automata on infinite trees

2021 ◽  
pp. 265-302
Author(s):  
Christof Löding
Keyword(s):  
Infinite Trees

scholarly journals Infinite Trees and the Future

1999 ◽  
pp. 379-391 ◽  
Author(s):  
Camil Demetrescu ◽  
Giuseppe Di Battista ◽  
Irene Finocchi ◽  
Giuseppe Liotta ◽  
Maurizio Patrignani ◽  
...  
Keyword(s):  
Infinite Trees ◽  
The Future

Four Integers whose Twelve Quotients Sum to Zero

1986 ◽  
Vol 38 (5) ◽  
pp. 1261-1280 ◽  
Author(s):  
John Leech
Keyword(s):  
Infinite Trees

This paper is devoted to the study of sets of four unequal integers ni such that the twelve quotients ni/nj(i ≠ j) of pairs of distinct members sum to zero. (Without the restriction i ≠ j the condition would be equivalent to (Σ ni)(Σ l/ni) = 0, of no great interest.) Constructions for these sets are given, and relations between them are studied. It is found that each set belongs to an orbit of six related sets, and that each such orbit is related to four neighbours, each of which is another orbit of six sets. A study is made of the graph formed by assigning a node to each orbit of six solutions and joining it to the nodes assigned to its four neighbours. This appears to comprise one component containing an infinity of cycles together with an infinite forest of infinite trees.

scholarly journals Fixed elements of infinite trees

1994 ◽  
Vol 130 (1-3) ◽  
pp. 97-102 ◽  
Author(s):  
Norbert Polat ◽  
Gert Sabidussi
Keyword(s):  
Infinite Trees

On well-quasi-ordering infinite trees – Nash–Williams's theorem revisited

2001 ◽  
Vol 130 (3) ◽  
pp. 401-408 ◽  
Author(s):  
DANIELA KÜHN
Keyword(s):  
Short Proof ◽  
Infinite Trees ◽  
Quasi Ordering

Nash–Williams proved that the infinite trees are well-quasi-ordered (indeed, better-quasi-ordered) under the topological minor relation. We combine ideas of several authors into a more accessible and essentially self-contained short proof.

Pointwise extensions of GSOS-defined operations

2011 ◽  
Vol 21 (2) ◽  
pp. 321-361 ◽  
Author(s):  
HELLE HVID HANSEN ◽  
BARTEK KLIN
Keyword(s):  
Operational Semantics ◽  
Infinite Trees ◽  
Structural Operational Semantics ◽  
Algebraic Operations ◽  
Abstract Specification

Final coalgebras capture system behaviours such as streams, infinite trees and processes. Algebraic operations on a final coalgebra can be defined by distributive laws (of a syntax functor Σ over a behaviour functor F). Such distributive laws correspond to abstract specification formats. One such format is a generalisation of the GSOS rules known from structural operational semantics of processes. We show that given an abstract GSOS specification ρ that defines operations σ on a final F-coalgebra, we can systematically construct a GSOS specification ρ that defines the pointwise extension σ of σ on a final FA-coalgebra. The construction relies on the addition of a family of auxiliary ‘buffer’ operations to the syntax. These buffer operations depend only on A, so the construction is uniform for all σ and F.

THE EFFECT OF THE NUMBER OF SUCCESSFUL PATHS IN A BÜCHI TREE AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 237-250
Author(s):  
D. BEAUQUIER ◽  
M. NIVAT ◽  
D. NIWIŃSKI
Keyword(s):  
Cardinal Number ◽  
Tree Automaton ◽  
Büchi Automata ◽  
Infinite Trees ◽  
Acceptance Condition ◽  
Tree Languages ◽  
Büchi Automaton ◽  
Buchi Automata ◽  
Computation Path

We modify an acceptance condition of Büchi automaton on infinite trees: rather than to require that each computation path is successful, we impose various restrictions on the number of successful paths in a run of the automaton on a tree. All these modifications alter the recognizing power of Büchi automata. We examine the classes induced by the acceptance conditions that require ≤α, ≥α, =α successful paths, where α is a cardinal number. It turns out that, except for some trivial cases, the “≤” classes are incomparable with the class Bü of Büchi acceptable tree languages, while the classes “≥” are strictly included in Bü.

Sign in / Sign up

Export Citation Format

Share Document