18,603 research outputs found
Improved bounds for testing Dyck languages
In this paper we consider the problem of deciding membership in Dyck
languages, a fundamental family of context-free languages, comprised of
well-balanced strings of parentheses. In this problem we are given a string of
length in the alphabet of parentheses of types and must decide if it is
well-balanced. We consider this problem in the property testing setting, where
one would like to make the decision while querying as few characters of the
input as possible.
Property testing of strings for Dyck language membership for , with a
number of queries independent of the input size , was provided in [Alon,
Krivelevich, Newman and Szegedy, SICOMP 2001]. Property testing of strings for
Dyck language membership for was first investigated in [Parnas, Ron
and Rubinfeld, RSA 2003]. They showed an upper bound and a lower bound for
distinguishing strings belonging to the language from strings that are far (in
terms of the Hamming distance) from the language, which are respectively (up to
polylogarithmic factors) the power and the power of the input size
.
Here we improve the power of in both bounds. For the upper bound, we
introduce a recursion technique, that together with a refinement of the methods
in the original work provides a test for any power of larger than .
For the lower bound, we introduce a new problem called Truestring Equivalence,
which is easily reducible to the -type Dyck language property testing
problem. For this new problem, we show a lower bound of to the power of
Conflicts and projections
This paper studies abstraction methods suitable to verify very large models of discrete-event systems to be nonconflicting. It compares the observer property to methods known from process algebra, namely to conflict equivalence and observation equivalence. The observer property is shown to be the property that corresponds to conflict equivalence in the case where natural projection is used for abstraction. In this case, the observer property turns out to be the least restrictive condition that can be imposed on natural projection to enable compositional reasoning about conflicts. The observer property is also shown to be closely related to observation equivalence. Several examples and propositions are presented to relate different aspects of these methods of abstraction
Verification of the observer property in discrete event systems
The observer property is an important condition to be satisfied by abstractions of Discrete Event System (DES) models. This technical note presents a new algorithm that tests if an abstraction of a DES obtained through natural projection has the observer property. The procedure, called OP-Verifier, can be applied to (potentially nondeterministic) automata, with no restriction on the existence of cycles of 'non-relevant' events. This procedure has quadratic complexity in the number of states. The performance of the algorithm is illustrated by a set of experiments
A Polynomial Time Algorithm for Deciding Branching Bisimilarity on Totally Normed BPA
Strong bisimilarity on normed BPA is polynomial-time decidable, while weak
bisimilarity on totally normed BPA is NP-hard. It is natural to ask where the
computational complexity of branching bisimilarity on totally normed BPA lies.
This paper confirms that this problem is polynomial-time decidable. To our
knowledge, in the presence of silent transitions, this is the first
bisimilarity checking algorithm on infinite state systems which runs in
polynomial time. This result spots an instance in which branching bisimilarity
and weak bisimilarity are both decidable but lie in different complexity
classes (unless NP=P), which is not known before.
The algorithm takes the partition refinement approach and the final
implementation can be thought of as a generalization of the previous algorithm
of Czerwi\'{n}ski and Lasota. However, unexpectedly, the correctness of the
algorithm cannot be directly generalized from previous works, and the
correctness proof turns out to be subtle. The proof depends on the existence of
a carefully defined refinement operation fitted for our algorithm and the
proposal of elaborately developed techniques, which are quite different from
previous works.Comment: 32 page
Deciding KAT and Hoare Logic with Derivatives
Kleene algebra with tests (KAT) is an equational system for program
verification, which is the combination of Boolean algebra (BA) and Kleene
algebra (KA), the algebra of regular expressions. In particular, KAT subsumes
the propositional fragment of Hoare logic (PHL) which is a formal system for
the specification and verification of programs, and that is currently the base
of most tools for checking program correctness. Both the equational theory of
KAT and the encoding of PHL in KAT are known to be decidable. In this paper we
present a new decision procedure for the equivalence of two KAT expressions
based on the notion of partial derivatives. We also introduce the notion of
derivative modulo particular sets of equations. With this we extend the
previous procedure for deciding PHL. Some experimental results are also
presented.Comment: In Proceedings GandALF 2012, arXiv:1210.202
Minimal DFAs for Testing Divisibility
We present and prove a theorem answering the question "how many states does a
minimal deterministic finite automaton (DFA) that recognizes the set of base-b
numbers divisible by k have?"Comment: LaTeX, 7 pages (corrected typo in new version
Composite repetition-aware data structures
In highly repetitive strings, like collections of genomes from the same
species, distinct measures of repetition all grow sublinearly in the length of
the text, and indexes targeted to such strings typically depend only on one of
these measures. We describe two data structures whose size depends on multiple
measures of repetition at once, and that provide competitive tradeoffs between
the time for counting and reporting all the exact occurrences of a pattern, and
the space taken by the structure. The key component of our constructions is the
run-length encoded BWT (RLBWT), which takes space proportional to the number of
BWT runs: rather than augmenting RLBWT with suffix array samples, we combine it
with data structures from LZ77 indexes, which take space proportional to the
number of LZ77 factors, and with the compact directed acyclic word graph
(CDAWG), which takes space proportional to the number of extensions of maximal
repeats. The combination of CDAWG and RLBWT enables also a new representation
of the suffix tree, whose size depends again on the number of extensions of
maximal repeats, and that is powerful enough to support matching statistics and
constant-space traversal.Comment: (the name of the third co-author was inadvertently omitted from
previous version
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