Showing papers on "Decision tree model published in 1991"

Complexity results for planning

Abstract: I describe several computational complexity results for planning, some of which identify tractable planning problems. The model of planning, called "propositional planning," is simple—conditions within operators are literals with no variables allowed. The different plan­ ning problems are defined by different restrictions on the preconditions and postconditions of operators. The main results are: Proposi­ tional planning is PSPACE-complete, even if operators are restricted to two positive (non-negated) preconditions and two postconditions, or if operators are restricted to one postcondi­ tion (with any number of preconditions). It is NP-complete if operators are restricted to positive postconditions, even if operators are restricted to one precondition and one posi­ tive postcondition. It is tractable in a few re­ stricted cases, one of which is if each opera­ tor is restricted to positive preconditions and one postcondition. The blocks-world problem, slightly modified, is a subproblem of this re­ stricted planning problem. 1 Introduction If the relationship between intelligence and computation is taken seriously, then intelligence cannot be explained by intractable theories because no intelligent creature has the time to perform intractable computations. Nor can intractable theories provide any guarantees about the performance of engineered systems. Presumably, robots don't have the time to perform intractable com­ putations either. Of course, heuristic theories are a valid approach if partial or approximate solutions are acceptable. How­ ever, my purpose is not to consider the relative merits of heuristic theories and tractable theories. Instead, I shall focus on formulating tractable planning problems. Planning is the reasoning task of finding a sequence of operators that achieve a goal from a given initial state. It is well-known that planning is intractable in general, and that several obstacles stand in the way [Chapman. 1987]. However, there are few results that provide clear dividing lines between tractable and in tractable planning. Below, I clarify a few of these dividing lines by analyzing the computational complexity of a planning problem and a variety of restricted versions, some of which are tractable. The model of planning, called "propositional planning ," is impoverished compared to working planners. It is intended to be a tool for theoretical analysis rather than programming convenience. Preconditions and post-conditions of operators are limited to being literals, i.e., letters or their negations. An initial state then can be represented as a finite set of letters, indicating that the corresponding conditions are initially true, and that all other relevant conditions are initially …

Rounds in communication complexity revisited

Abstract: The $k$-round two-party communication complexity was studied in the deterministic model by [14] and [4] and in the probabilistic model by [20] and [6]. We present new lower bounds that give (1) randomization is more powerful than determinism in $k$-round protocols, and (2) an explicit function which exhibits an exponential gap between its $k$ and $(k-1)$-round randomized complexity. We also study the three party communication model, and exhibit an exponential gap in 3-round protocols that differ in the starting player. Finally, we show new connections of these questions to circuit complexity, that motivate further work in this direction.

Super-logarithmic Depth Lower Bounds via Direct Sum in Communication Complexity (Preliminary Version)

Abstract: Is it easier to solve two communication problems to- gether than separately? This question is related to the complexity of the composition of boolean functions. Based on this relationship, an approach to separating NC' from P is outlined. Furthermore, it is shown that the approach provides a new proof of the separation of monotone NC' from monotone P.

Search problems in the decision tree model

Abstract: The relative power of determinism, randomness, and nondeterminism for search problems in the Boolean decision tree model is studied. It is shown that the CNF search problem is complete for all the variants of decision trees. It is then shown that the gaps between the nondeterministic, the randomized, and the deterministic complexities can be arbitrarily large for search problems. The special case of nondeterministic complexity is discussed. >

Designing storage efficient decision trees

Abstract: The problem of designing storage-efficient decision trees from decision tables is examined. It is shown that for most cases, the construction of the storage optimal decision tree is an NP-complete problem, and therefore a heuristic approach to the problem is necessary. A systematic procedure analogous to the information-theoretic heuristic is developed. The algorithm has low computational complexity and performs well experimentally. >

On the Computational Complexity of Incremental Algorithms

Abstract: Our results, together with some previously known ones, shed light on the organization of the complexity hierarchy that exists when incremental-computation problems are classified according to their incremental complexity with respect to locally persistent algorithms. In particular, these results separate the classes of P-time incremental problems, inherently Exp~ time incremental problems, and non-incremental problems.

Optimization of the decision tree

Abstract: An approach is presented to the optimization of decision trees. A decision tree is considered optimal if it correctly classifies the known data set and has the minimal number of nodes. It is shown that it is important to decide the right order of attributes to test, for this can reduce the number of checking nodes in a decision tree. >

Efficient algorithms for selection of recovery points in tree task models

Abstract: Efficient solutions to the problem of optimally selecting recovery points are developed. The solutions are intended for models of computation in which task precedence has a tree structure and a task may fail due to the presence of faults. An algorithm to minimize the expected computation time of the task system under a uniprocessor environment has been developed for the binary tree model. The algorithm has time complexity of O(N/sub 2/), where N is the number of tasks, while previously reported procedures have exponential time requirements. The results are generalized for an arbitrary tree model. >

Lower bounds for the non-linear complexity of algebraic computation trees with integer inputs

Abstract: Andrew Yao proved some lower bounds for algebraic computation trees with integer inputs. In his key result he proved bounds on the number of components of the leaf space of a homogeneous decision tree derived from a computation tree. In this paper we present a shorter and more conceptual proof. We introduce the concept of aregulated tree as a generalization of a regular tree which has the advantage of allowing the same lower bounds on the non-linear portion of the complexity. The proof is an application of a result of Ben-Or.

A parallel sorting algorithm for a novel model of computation

Abstract: The computational complexity of a parallel algorithm depends critically on the model of computation. We describe a simple and elegant rule-based model of computation in which processors apply rules asynchronously to pairs of objects from a global object space. Application of a rule to a pair of objects results in the creation of a new object if the objects satisfy the guard of the rule. The model can be efficiently implemented as a novel MIMD array processor architecture, the Intersecting Broadcast Machine. For this model of computation, we describe an efficient parallel sorting algorithm based on mergesort. The computational complexity of the sorting algorithm isO(nlog2n), comparable to that for specialized sorting networks and an improvement on theO(n1.5) complexity of conventional mesh-connected array processors.

Reduction of dimensionality of an optimal decision table conversion algorithm

Abstract: A dynamic programming algorithm for converting decision tables to optimal decision trees is analyzed. The complexity of the algorithm may be defined as the dimension of the domain of the minimal-cost functional. Upper bounds for this complexity are derived under various assumptions. Methods of reducing the dimensionality of the problem utilizing lower bounds for decision costs are also discussed.

Concise Papers Efficient Algorithms For Selection of Recovery Points in lkee Task Models

Abstract: Absfruct-In this note we develop efficient solutions to the problem of optimally selecting recovery points. These solutions are intended for models of computation in which task precedence has a tree structure and a task may fail due to the presence of faults. For the binary tree model, an algorithm to minimize the expected computation time of the task system under a uniprocessor environment has been developed. The algorithm has time complexity of O(N’), where N is the number of tasks, while previously reported procedures have exponential time requirements. The results have been generalized for an arbitrary tree model. Index Terms-Checkpoints, dynamic programming, emr recovery, reliability, rollback.