15,222 research outputs found
Dynamic Set Intersection
Consider the problem of maintaining a family of dynamic sets subject to
insertions, deletions, and set-intersection reporting queries: given , report every member of in any order. We show that in the word
RAM model, where is the word size, given a cap on the maximum size of
any set, we can support set intersection queries in
expected time, and updates in expected time. Using this algorithm
we can list all triangles of a graph in
expected time, where and
is the arboricity of . This improves a 30-year old triangle enumeration
algorithm of Chiba and Nishizeki running in time.
We provide an incremental data structure on that supports intersection
{\em witness} queries, where we only need to find {\em one} .
Both queries and insertions take O\paren{\sqrt \frac{N}{w/\log^2 w}} expected
time, where . Finally, we provide time/space tradeoffs for
the fully dynamic set intersection reporting problem. Using words of space,
each update costs expected time, each reporting query
costs expected time where
is the size of the output, and each witness query costs expected time.Comment: Accepted to WADS 201
Towards Parameterized Regular Type Inference Using Set Constraints
We propose a method for inferring \emph{parameterized regular types} for
logic programs as solutions for systems of constraints over sets of finite
ground Herbrand terms (set constraint systems). Such parameterized regular
types generalize \emph{parametric} regular types by extending the scope of the
parameters in the type definitions so that such parameters can relate the types
of different predicates. We propose a number of enhancements to the procedure
for solving the constraint systems that improve the precision of the type
descriptions inferred. The resulting algorithm, together with a procedure to
establish a set constraint system from a logic program, yields a program
analysis that infers tighter safe approximations of the success types of the
program than previous comparable work, offering a new and useful efficiency vs.
precision trade-off. This is supported by experimental results, which show the
feasibility of our analysis
The Complexity of Codiagnosability for Discrete Event and Timed Systems
In this paper we study the fault codiagnosis problem for discrete event
systems given by finite automata (FA) and timed systems given by timed automata
(TA). We provide a uniform characterization of codiagnosability for FA and TA
which extends the necessary and sufficient condition that characterizes
diagnosability. We also settle the complexity of the codiagnosability problems
both for FA and TA and show that codiagnosability is PSPACE-complete in both
cases. For FA this improves on the previously known bound (EXPTIME) and for TA
it is a new result. Finally we address the codiagnosis problem for TA under
bounded resources and show it is 2EXPTIME-complete.Comment: 24 pages
Distributed Graph Automata and Verification of Distributed Algorithms
Combining ideas from distributed algorithms and alternating automata, we
introduce a new class of finite graph automata that recognize precisely the
languages of finite graphs definable in monadic second-order logic. By
restricting transitions to be nondeterministic or deterministic, we also obtain
two strictly weaker variants of our automata for which the emptiness problem is
decidable. As an application, we suggest how suitable graph automata might be
useful in formal verification of distributed algorithms, using Floyd-Hoare
logic.Comment: 26 pages, 6 figures, includes a condensed version of the author's
Master's thesis arXiv:1404.6503. (This version of the article (v2) is
identical to the previous one (v1), except for minor changes in phrasing.
On Measuring Non-Recursive Trade-Offs
We investigate the phenomenon of non-recursive trade-offs between
descriptional systems in an abstract fashion. We aim at categorizing
non-recursive trade-offs by bounds on their growth rate, and show how to deduce
such bounds in general. We also identify criteria which, in the spirit of
abstract language theory, allow us to deduce non-recursive tradeoffs from
effective closure properties of language families on the one hand, and
differences in the decidability status of basic decision problems on the other.
We develop a qualitative classification of non-recursive trade-offs in order to
obtain a better understanding of this very fundamental behaviour of
descriptional systems
History-Register Automata
Programs with dynamic allocation are able to create and use an unbounded
number of fresh resources, such as references, objects, files, etc. We propose
History-Register Automata (HRA), a new automata-theoretic formalism for
modelling such programs. HRAs extend the expressiveness of previous approaches
and bring us to the limits of decidability for reachability checks. The
distinctive feature of our machines is their use of unbounded memory sets
(histories) where input symbols can be selectively stored and compared with
symbols to follow. In addition, stored symbols can be consumed or deleted by
reset. We show that the combination of consumption and reset capabilities
renders the automata powerful enough to imitate counter machines, and yields
closure under all regular operations apart from complementation. We moreover
examine weaker notions of HRAs which strike different balances between
expressiveness and effectiveness.Comment: LMCS (improved version of FoSSaCS
- …