2,140 research outputs found
The RAM equivalent of P vs. RP
One of the fundamental open questions in computational complexity is whether
the class of problems solvable by use of stochasticity under the Random
Polynomial time (RP) model is larger than the class of those solvable in
deterministic polynomial time (P). However, this question is only open for
Turing Machines, not for Random Access Machines (RAMs).
Simon (1981) was able to show that for a sufficiently equipped Random Access
Machine, the ability to switch states nondeterministically does not entail any
computational advantage. However, in the same paper, Simon describes a
different (and arguably more natural) scenario for stochasticity under the RAM
model. According to Simon's proposal, instead of receiving a new random bit at
each execution step, the RAM program is able to execute the pseudofunction
, which returns a uniformly distributed random integer in the
range . Whether the ability to allot a random integer in this fashion is
more powerful than the ability to allot a random bit remained an open question
for the last 30 years.
In this paper, we close Simon's open problem, by fully characterising the
class of languages recognisable in polynomial time by each of the RAMs
regarding which the question was posed. We show that for some of these,
stochasticity entails no advantage, but, more interestingly, we show that for
others it does.Comment: 23 page
A Case Study in Refactoring Functional Programs
Refactoring is the process of redesigning existing code without changing its functionality. Refactoring has recently come to prominence in the OO community. In this paper we explore the prospects for refactoring functional programs. Our paper centres on the case study of refactoring a 400 line Haskell program written by one of our students. The case study illustrates the type and variety of program manipulations involved in refactoring. Similarly to other program transformations, refactorings are based on program equivalences, and thus ultimately on language semantics. In the context of functional languages, refactorings can be based on existing theory and program analyses. However, the use of program transformations for program restructuring emphasises a different kind of transformation from the more traditional derivation or optimisation: characteristically, they often require wholesale changes to a collection of modules, and although they are best controlled by programmers, their application may require nontrivial semantic analyses. The paper also explores the background to refactoring, provides a taxonomy for describing refactorings and draws some conclusions about refactoring for functional programs
Reasoning with Forest Logic Programs and f-hybrid Knowledge Bases
Open Answer Set Programming (OASP) is an undecidable framework for
integrating ontologies and rules. Although several decidable fragments of OASP
have been identified, few reasoning procedures exist. In this article, we
provide a sound, complete, and terminating algorithm for satisfiability
checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules
have a tree shape and allow for inequality atoms and constants. The algorithm
establishes a decidability result for FoLPs. Although believed to be decidable,
so far only the decidability for two small subsets of FoLPs, local FoLPs and
acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a
hybrid framework where \SHOQ{} knowledge bases and forest logic programs
co-exist, and we show that reasoning with such knowledge bases can be reduced
to reasoning with forest logic programs only. We note that f-hybrid knowledge
bases do not require the usual (weakly) DL-safety of the rule component,
providing thus a genuine alternative approach to current integration approaches
of ontologies and rules
Logic Programming for Finding Models in the Logics of Knowledge and its Applications: A Case Study
The logics of knowledge are modal logics that have been shown to be effective
in representing and reasoning about knowledge in multi-agent domains.
Relatively few computational frameworks for dealing with computation of models
and useful transformations in logics of knowledge (e.g., to support multi-agent
planning with knowledge actions and degrees of visibility) have been proposed.
This paper explores the use of logic programming (LP) to encode interesting
forms of logics of knowledge and compute Kripke models. The LP modeling is
expanded with useful operators on Kripke structures, to support multi-agent
planning in the presence of both world-altering and knowledge actions. This
results in the first ever implementation of a planner for this type of complex
multi-agent domains.Comment: 16 pages, 1 figure, International Conference on Logic Programming
201
Relations between the minors of a generic matrix
It is well-known that the Pl\"ucker relations generate the ideal of relations
of the maximal minors of a generic matrix. In this paper we discuss the
relations between minors of a (non-maximal) fixed size. We will exhibit minimal
relations in degrees 2 (non-Pl\"ucker in general) and 3, and give some evidence
for our conjecture that we have found the generating system of the ideal of
relations. The approach is through the representation theory of the general
linear group.Comment: Final version, minor changes, to appear in Advances in Mathematic
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