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# Regular matching problems for infinite trees

## March 25, 2021 @ 10:00 am - 12:00 pm

Title: Regular matching problems for infinite trees

Speaker: Mircea Marin (West University of Timișoara)

Abstract:

We study the matching problem “∃σ:σ(L)⊆R?” where L and R are regular tree languages over finite ranked alphabets X and Σ respectively, and σ is a substitution such that σ(x) is a set of trees in T(Σ∪H)∖H for all x∈X. Here, H denotes a set of holes which are used to define a concatenation of trees. Conway studied this problem in the special case for languages of finite words in his classical textbook Regular algebra and finite machines and showed that if L and R are regular, then the problem “∃σ:∀x∈X:σ(x)≠∅∧σ(L)⊆R?” is decidable. Moreover, there are only finitely many maximal solutions, which are regular and effectively computable. We extend Conway’s results when L and R are regular languages of finite and infinite trees, and language substitution is applied inside-out. We show that if L⊆T(X) and R⊆T(Σ) are regular tree languages then the problem “∃σ∀x∈X:σ(x)≠∅∧σio(L)⊆R?” is decidable. Moreover, there are only finitely many maximal solutions, which are regular and effectively computable. The corresponding question for the outside-in extension σoi remains open, even in the restricted setting of finite trees. Our main result is the decidability of “∃σ:σio(L)⊆R?” if R is regular and L belongs to a class of tree languages closed under intersection with regular sets. Such a special case pops up if L is context-free.
This is joint work with Carlos Camino, Volker Diekert, Besik Dundua and Géraud Sénizergues.

References:

[1] C. Camino, V. Diekert, B. Dundua, M. Marin, G. Sénizergues, Regular matching problems for infinite trees. arXiv:2004.09926 [cs.FL], 2021.

## Details

Date:
March 25, 2021
Time:
10:00 am - 12:00 pm
Event Category:
Website:
https://cs.unibuc.ro/~lleustean/Seminar-Logic/seminar-logic.html