3 research outputs found
The descriptive complexity approach to LOGCFL
Building upon the known generalized-quantifier-based first-order
characterization of LOGCFL, we lay the groundwork for a deeper investigation.
Specifically, we examine subclasses of LOGCFL arising from varying the arity
and nesting of groupoidal quantifiers. Our work extends the elaborate theory
relating monoidal quantifiers to NC1 and its subclasses. In the absence of the
BIT predicate, we resolve the main issues: we show in particular that no single
outermost unary groupoidal quantifier with FO can capture all the context-free
languages, and we obtain the surprising result that a variant of Greibach's
``hardest context-free language'' is LOGCFL-complete under quantifier-free
BIT-free projections. We then prove that FO with unary groupoidal quantifiers
is strictly more expressive with the BIT predicate than without. Considering a
particular groupoidal quantifier, we prove that first-order logic with majority
of pairs is strictly more expressive than first-order with majority of
individuals. As a technical tool of independent interest, we define the notion
of an aperiodic nondeterministic finite automaton and prove that FO
translations are precisely the mappings computed by single-valued aperiodic
nondeterministic finite transducers.Comment: 10 pages, 1 figur
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science