131 research outputs found
Operations on Automata with All States Final
We study the complexity of basic regular operations on languages represented
by incomplete deterministic or nondeterministic automata, in which all states
are final. Such languages are known to be prefix-closed. We get tight bounds on
both incomplete and nondeterministic state complexity of complement,
intersection, union, concatenation, star, and reversal on prefix-closed
languages.Comment: In Proceedings AFL 2014, arXiv:1405.527
From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity
The equivalence of finite automata and regular expressions dates back to the
seminal paper of Kleene on events in nerve nets and finite automata from 1956.
In the present paper we tour a fragment of the literature and summarize results
on upper and lower bounds on the conversion of finite automata to regular
expressions and vice versa. We also briefly recall the known bounds for the
removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free
nondeterministic devices. Moreover, we report on recent results on the average
case descriptional complexity bounds for the conversion of regular expressions
to finite automata and brand new developments on the state elimination
algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527
The Magic Number Problem for Subregular Language Families
We investigate the magic number problem, that is, the question whether there
exists a minimal n-state nondeterministic finite automaton (NFA) whose
equivalent minimal deterministic finite automaton (DFA) has alpha states, for
all n and alpha satisfying n less or equal to alpha less or equal to exp(2,n).
A number alpha not satisfying this condition is called a magic number (for n).
It was shown in [11] that no magic numbers exist for general regular languages,
while in [5] trivial and non-trivial magic numbers for unary regular languages
were identified. We obtain similar results for automata accepting subregular
languages like, for example, combinational languages, star-free, prefix-,
suffix-, and infix-closed languages, and prefix-, suffix-, and infix-free
languages, showing that there are only trivial magic numbers, when they exist.
For finite languages we obtain some partial results showing that certain
numbers are non-magic.Comment: In Proceedings DCFS 2010, arXiv:1008.127
Nondeterministic State Complexity for Suffix-Free Regular Languages
We investigate the nondeterministic state complexity of basic operations for
suffix-free regular languages. The nondeterministic state complexity of an
operation is the number of states that are necessary and sufficient in the
worst-case for a minimal nondeterministic finite-state automaton that accepts
the language obtained from the operation. We consider basic operations
(catenation, union, intersection, Kleene star, reversal and complementation)
and establish matching upper and lower bounds for each operation. In the case
of complementation the upper and lower bounds differ by an additive constant of
two.Comment: In Proceedings DCFS 2010, arXiv:1008.127
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