18 research outputs found
Structure Theorem and Strict Alternation Hierarchy for FO^2 on Words
It is well-known that every first-order property on words is expressible
using at most three variables. The subclass of properties expressible with only
two variables is also quite interesting and well-studied. We prove precise
structure theorems that characterize the exact expressive power of first-order
logic with two variables on words. Our results apply to both the case with and
without a successor relation. For both languages, our structure theorems show
exactly what is expressible using a given quantifier depth, n, and using m
blocks of alternating quantifiers, for any m \leq n. Using these
characterizations, we prove, among other results, that there is a strict
hierarchy of alternating quantifiers for both languages. The question whether
there was such a hierarchy had been completely open. As another consequence of
our structural results, we show that satisfiability for first-order logic with
two variables without successor, which is NEXP-complete in general, becomes
NP-complete once we only consider alphabets of a bounded size
One-Dimensional Fragment Over Words and Trees
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.Peer reviewe
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems