One-Dimensional Fragment over Words and Trees
Logic in Computer Science
2024-04-08 v1
Abstract
One-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential (universal) quantifiers that leave at most one variable free. We investigate this fragment over words and trees, presenting a complete classification of the complexity of its satisfiability problem for various navigational signatures, and comparing its expressive power with other important formalisms. These include the two-variable fragment with counting and the unary negation fragment.
Cite
@article{arxiv.2110.02678,
title = {One-Dimensional Fragment over Words and Trees},
author = {Emanuel Kieronski and Antti Kuusisto},
journal= {arXiv preprint arXiv:2110.02678},
year = {2024}
}
Comments
Full version of [1] Emanuel Kieronski: One-Dimensional Logic over Words. CSL 2016: 38:1-38:15 [2] Emanuel Kieronski, Antti Kuusisto: One-Dimensional Logic over Trees. MFCS 2017: 64:1-64:13