5 research outputs found
Bounds on the Automata Size for Presburger Arithmetic
Automata provide a decision procedure for Presburger arithmetic. However,
until now only crude lower and upper bounds were known on the sizes of the
automata produced by this approach. In this paper, we prove an upper bound on
the the number of states of the minimal deterministic automaton for a
Presburger arithmetic formula. This bound depends on the length of the formula
and the quantifiers occurring in the formula. The upper bound is established by
comparing the automata for Presburger arithmetic formulas with the formulas
produced by a quantifier elimination method. We also show that our bound is
tight, even for nondeterministic automata. Moreover, we provide optimal
automata constructions for linear equations and inequations
On the Use of Quasiorders in Formal Language Theory
In this thesis we use quasiorders on words to offer a new perspective on two
well-studied problems from Formal Language Theory: deciding language inclusion
and manipulating the finite automata representations of regular languages.
First, we present a generic quasiorder-based framework that, when instantiated
with different quasiorders, yields different algorithms (some of them new) for
deciding language inclusion. We then instantiate this framework to devise an
efficient algorithm for searching with regular expressions on
grammar-compressed text. Finally, we define a framework of quasiorder-based
automata constructions to offer a new perspective on residual automata.Comment: PhD thesi