35 research outputs found
Affine completeness of some free binary algebras
A function on an algebra is congruence preserving if, for any congruence, it
maps pairs of congruent elements onto pairs of congruent elements. An algebra
is said to be affine complete if every congruence preserving function is a
polynomial function. We show that the algebra of (possibly empty) binary trees
whose leaves are labeled by letters of an alphabet containing at least one
letter, and the free monoid on an alphabet containing at least two letters are
affine complete
Inf-datalog, Modal Logic and Complexities
Inf-Datalog
extends the usual least fixpoint semantics of Datalog with greatest
fixpoint semantics: we defined inf-Datalog and characterized the
expressive power of various fragments of inf-Datalog in [CITE].
In the present paper, we study the
complexity of query evaluation on finite models
for (various fragments of) inf-Datalog.
We deduce a unified and elementary proof that global model-checking
(i.e. computing all nodes satisfying a formula in a given structure) has
1. quadratic data complexity in time
and linear program complexity in space
for CTL and alternation-free modal ÎĽ-calculus, and
2. linear-space (data and program) complexities,
linear-time program complexity
and polynomial-time data complexity
for Lµk (modal μ-calculus with fixed alternation-depth at most k)
INF-DATALOG, MODAL LOGIC AND COMPLEXITIES
Inf-Datalog extends the usual least fixpoint semantics of Datalog with greatest fixpoint semantics: we defined inf-Datalog and characterized the expressive power of various fragments of inf-Datalog in [GFAA03]. In the present paper, we study the complexity of query evaluation on finite models for (various fragments of) inf-Datalog. We deduce a unified and elementary proof that global model-checking (i.e. computing all nodes satisfying a formula in a given structure) has 1. quadratic data complexity in time and linear program complexity in space for CTL and alternation-free modal µ-calculus, and 2. linearspace (data and program) complexities, linear-time program complexity and polynomial-time data complexity for Lµk (modal µ-calculus with fixed alternation-depth at most k)