3,729 research outputs found
On Exact and Approximate Solutions for Hard Problems: An Alternative Look
We discuss in an informal, general audience style the da Costa-Doria conjecture about the independence of the P = NP hypothesis and try to briefly assess its impact on practical situations in economics. The paper concludes with a discussion of the Coppe-Cosenza procedure, which is an approximate, partly heuristic algorithm for allocation problems.P vs. NP , allocation problem, assignment problem, traveling salesman, exact solution for NP problems, approximate solutions for NP problems, undecidability, incompleteness
Regression with respect to sensing actions and partial states
In this paper, we present a state-based regression function for planning
domains where an agent does not have complete information and may have sensing
actions. We consider binary domains and employ the 0-approximation [Son & Baral
2001] to define the regression function. In binary domains, the use of
0-approximation means using 3-valued states. Although planning using this
approach is incomplete with respect to the full semantics, we adopt it to have
a lower complexity. We prove the soundness and completeness of our regression
formulation with respect to the definition of progression. More specifically,
we show that (i) a plan obtained through regression for a planning problem is
indeed a progression solution of that planning problem, and that (ii) for each
plan found through progression, using regression one obtains that plan or an
equivalent one. We then develop a conditional planner that utilizes our
regression function. We prove the soundness and completeness of our planning
algorithm and present experimental results with respect to several well known
planning problems in the literature.Comment: 38 page
Efficient Open World Reasoning for Planning
We consider the problem of reasoning and planning with incomplete knowledge
and deterministic actions. We introduce a knowledge representation scheme
called PSIPLAN that can effectively represent incompleteness of an agent's
knowledge while allowing for sound, complete and tractable entailment in
domains where the set of all objects is either unknown or infinite. We present
a procedure for state update resulting from taking an action in PSIPLAN that is
correct, complete and has only polynomial complexity. State update is performed
without considering the set of all possible worlds corresponding to the
knowledge state. As a result, planning with PSIPLAN is done without direct
manipulation of possible worlds. PSIPLAN representation underlies the PSIPOP
planning algorithm that handles quantified goals with or without exceptions
that no other domain independent planner has been shown to achieve. PSIPLAN has
been implemented in Common Lisp and used in an application on planning in a
collaborative interface.Comment: 39 pages, 13 figures. to appear in Logical Methods in Computer
Scienc
A State-Based Regression Formulation for Domains with Sensing Actions<br> and Incomplete Information
We present a state-based regression function for planning domains where an
agent does not have complete information and may have sensing actions. We
consider binary domains and employ a three-valued characterization of domains
with sensing actions to define the regression function. We prove the soundness
and completeness of our regression formulation with respect to the definition
of progression. More specifically, we show that (i) a plan obtained through
regression for a planning problem is indeed a progression solution of that
planning problem, and that (ii) for each plan found through progression, using
regression one obtains that plan or an equivalent one.Comment: 34 pages, 7 Figure
Sampling-based Algorithms for Optimal Motion Planning
During the last decade, sampling-based path planning algorithms, such as
Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have
been shown to work well in practice and possess theoretical guarantees such as
probabilistic completeness. However, little effort has been devoted to the
formal analysis of the quality of the solution returned by such algorithms,
e.g., as a function of the number of samples. The purpose of this paper is to
fill this gap, by rigorously analyzing the asymptotic behavior of the cost of
the solution returned by stochastic sampling-based algorithms as the number of
samples increases. A number of negative results are provided, characterizing
existing algorithms, e.g., showing that, under mild technical conditions, the
cost of the solution returned by broadly used sampling-based algorithms
converges almost surely to a non-optimal value. The main contribution of the
paper is the introduction of new algorithms, namely, PRM* and RRT*, which are
provably asymptotically optimal, i.e., such that the cost of the returned
solution converges almost surely to the optimum. Moreover, it is shown that the
computational complexity of the new algorithms is within a constant factor of
that of their probabilistically complete (but not asymptotically optimal)
counterparts. The analysis in this paper hinges on novel connections between
stochastic sampling-based path planning algorithms and the theory of random
geometric graphs.Comment: 76 pages, 26 figures, to appear in International Journal of Robotics
Researc
An overview of decision table literature 1982-1995.
This report gives an overview of the literature on decision tables over the past 15 years. As much as possible, for each reference, an author supplied abstract, a number of keywords and a classification are provided. In some cases own comments are added. The purpose of these comments is to show where, how and why decision tables are used. The literature is classified according to application area, theoretical versus practical character, year of publication, country or origin (not necessarily country of publication) and the language of the document. After a description of the scope of the interview, classification results and the classification by topic are presented. The main body of the paper is the ordered list of publications with abstract, classification and comments.
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