3,754 research outputs found
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
Random Generation and Enumeration of Accessible Determinisitic Real-time Pushdown Automata
This papers presents a general framework for the uniform random generation of
deterministic real-time accessible pushdown automata. A polynomial time
algorithm to randomly generate a pushdown automaton having a fixed stack
operations total size is proposed. The influence of the accepting condition
(empty stack, final state) on the reachability of the generated automata is
investigated.Comment: Frank Drewes. CIAA 2015, Aug 2015, Umea, Sweden. Springer, 9223,
pp.12, 2015, Implementation and Application of Automata - 20th International
Conferenc
Incomplete Transition Complexity of Basic Operations on Finite Languages
The state complexity of basic operations on finite languages (considering
complete DFAs) has been in studied the literature. In this paper we study the
incomplete (deterministic) state and transition complexity on finite languages
of boolean operations, concatenation, star, and reversal. For all operations we
give tight upper bounds for both description measures. We correct the published
state complexity of concatenation for complete DFAs and provide a tight upper
bound for the case when the right automaton is larger than the left one. For
all binary operations the tightness is proved using family languages with a
variable alphabet size. In general the operational complexities depend not only
on the complexities of the operands but also on other refined measures.Comment: 13 page
Edit Distance for Pushdown Automata
The edit distance between two words is the minimal number of word
operations (letter insertions, deletions, and substitutions) necessary to
transform to . The edit distance generalizes to languages
, where the edit distance from to
is the minimal number such that for every word from
there exists a word in with edit distance at
most . We study the edit distance computation problem between pushdown
automata and their subclasses. The problem of computing edit distance to a
pushdown automaton is undecidable, and in practice, the interesting question is
to compute the edit distance from a pushdown automaton (the implementation, a
standard model for programs with recursion) to a regular language (the
specification). In this work, we present a complete picture of decidability and
complexity for the following problems: (1)~deciding whether, for a given
threshold , the edit distance from a pushdown automaton to a finite
automaton is at most , and (2)~deciding whether the edit distance from a
pushdown automaton to a finite automaton is finite.Comment: An extended version of a paper accepted to ICALP 2015 with the same
title. The paper has been accepted to the LMCS journa
Comparator automata in quantitative verification
The notion of comparison between system runs is fundamental in formal
verification. This concept is implicitly present in the verification of
qualitative systems, and is more pronounced in the verification of quantitative
systems. In this work, we identify a novel mode of comparison in quantitative
systems: the online comparison of the aggregate values of two sequences of
quantitative weights. This notion is embodied by {\em comparator automata}
({\em comparators}, in short), a new class of automata that read two infinite
sequences of weights synchronously and relate their aggregate values.
We show that {aggregate functions} that can be represented with B\"uchi
automaton result in comparators that are finite-state and accept by the B\"uchi
condition as well. Such {\em -regular comparators} further lead to
generic algorithms for a number of well-studied problems, including the
quantitative inclusion and winning strategies in quantitative graph games with
incomplete information, as well as related non-decision problems, such as
obtaining a finite representation of all counterexamples in the quantitative
inclusion problem.
We study comparators for two aggregate functions: discounted-sum and
limit-average. We prove that the discounted-sum comparator is -regular
iff the discount-factor is an integer. Not every aggregate function, however,
has an -regular comparator. Specifically, we show that the language of
sequence-pairs for which limit-average aggregates exist is neither
-regular nor -context-free. Given this result, we introduce the
notion of {\em prefix-average} as a relaxation of limit-average aggregation,
and show that it admits -context-free comparators
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