Showing papers on "Decision tree model published in 1993"

Learning decision trees using the Fourier spectrum

Abstract: This work gives a polynomial time algorithm for learning decision trees with respect to the uniform distribution. (This algorithm uses membership queries.) The decision tree model that is considered is an extension of the traditional boolean decision tree model that allows linear operations in each node (i.e., summation of a subset of the input variables over $GF(2)$).This paper shows how to learn in polynomial time any function that can be approximated (in norm $L_2 $) by a polynomially sparse function (i.e., a function with only polynomially many nonzero Fourier coefficients). The authors demonstrate that any function f whose $L_1 $-norm (i.e., the sum of absolute value of the Fourier coefficients) is polynomial can be approximated by a polynomially sparse function, and prove that boolean decision trees with linear operations are a subset of this class of functions. Moreover, it is shown that the functions with polynomial $L_1 $-norm can be learned deterministically.The algorithm can also exactly identi...

The Complexity of Set Constraints

Abstract: Set constraints are relations between sets of terms. They have been used extensively in various applications in program analysis and type inference. We present several results on the computational complexity of solving systems of set constraints. The systems we study form a natural complexity hierarchy depending on the form of the constraint language.

Stratified functional programs and computational complexity

Abstract: Synopsis. We develop two notions of stratified recur

A serial complexity measure of neural networks

Abstract: The most common methodology of neural network analysis is that of simulation since as of yet there is no common formal framework. Towards this end, one measure of serial algorithms is adopted, i.e., that of serial computational complexity. It is applied to the analysis of neural networks. Various networks are analyzed and their complexity is derived, thus providing insight as to their computational requirements. >

Bounds on tradeoffs between randomness and communication complexity

Abstract: The power of randomness in improving the efficiency (or even possibility) of computations has been demonstrated in numerous contexts. A fundamental question ishow much randomness is required for these improvements, or how does the improvement grow as a function of the amount of randomness allowed. This quantitative question, restricted to the context of communication complexity, is the focus of our paper. We prove general lower bounds on the amount of randomness used in randomized protocols for computing a functionf, the input of which is split between two parties. The bounds depend on the number of bits communicated and the deterministic communication complexity off. Four models for communication complexity are considered: the random input of the parties may be public or private, and the communication may be one-way or two-way. (Unbounded advantage is allowed.) The bounds are shown to be tight; i.e., we demonstrate functions and protocols for these functions which meet the above bounds up to a constant factor. We do this for all the models, for all values of the deterministic communication complexity, and for all possible quantities of bits communicated.

Lower Bounds for One-way Probabilistic Communication Complexity

Abstract: We prove three different types of complexity lower bounds for the one-way unbounded-error and bounded-error error probabilistic communication protocols for boolean functions The lower bounds are proved for arbitrary boolean functions in the common way in terms of the deterministic communication complexity of functions and in terms of the notion “probabilistic communication characteristic” that we define

Point Probe Decision Trees for Geometric Concept Classes

Abstract: A fundamental problem in model-based computer vision is that of identifying to which of a given set of concept classes of geometric models an observed model belongs. Considering a “probe” to be an oracle that tells whether or not the observed model is present at a given point in an image, we study the problem of computing efficient strategies (“decision trees”) for probing an image, with the goal to minimize the number of probes necessary (in the worst case) to determine in which class the observed model belongs. We prove a hardness result and give strategies that obtain decision trees whose height is within a log factor of optimal.

Hierarchical Matching Beats The Non-Wildcard and Interpretation Tree Model Matching Algorithms

Abstract: In Fisher[l] we introduced a non-wildcard model matching algorithm that has speed advantages over the standard Interpretation Tree model matching algorithm. This paper describes a hierarchical model-matching algorithm that has improved performance over both the standard and non-wildcard algorithms.

On multi-party communication complexity of random functions

Abstract: We prove that almost a.ll Boolean function has a high k-party communication complexity. The 2-party case was settled by Papadimitriou and Sip&er [PS]. Proving the k-party esse needs a deeper investigation of the underlying structure of the k-cylinderintersectionsj (the 2-cylinder-intersections are the rectangles). First we examine the basic properties of k-cylinder-intersections, then an upper estimation is given for their number, which facilitates to prove the lower-bound theorem for the kparty communica.tion complexity of random Boolean functions. In the last section we extend our results to communication protocols, which are correct only on mo&t of the inputs. Address: Ma.x Planck Institute for Computer Science, Im Stadtwald, D-66123 Sa.a.rbruecken, GERMANYj email: grolmusz@mpi-sb.mpg.de

Complexity measures for testing binary keystreams

Abstract: The complexity measures that have been proposed to test binary keystreams for use in stream cipher cryptosystems fall into two categories. Measures in the first category determine the size of a specific tool required to produce the sequence, for example the Turing-Kolmogorov-Chaitin complexity, the linear complexity, and the maximum order complexity. Measures in the second category are related to patterns that appear in the sequence, for example the Ziv-Lempel complexity. As measures in the two categories have different motivations, they often react differently to sequences with special structure. We will review these measures and discuss their reaction to certain types of sequences. We next present a new complexity measure called the pattern counting complexity measure. This new measure is also related to the patterns that appear in the sequence. However unlike the Ziv-Lempel complexity measure, the pattern counting complexity measure is easy to describe and is easy to understand intuitively. The new measure also possesses some desirable characteristics in terms of consistency. Like the Ziv-Lempel complexity and the maximum order complexity, the distribution of the complexity and the distribution of the jumps in the complexity profile of random sequences have been difficult to compute exactly for the new measure. We will present a function that approximates the distribution of the size of the jumps in the pattern counting complexity profile of a random sequence and demonstrate how this function can be used to approximate the expected value of the pattern counting complexity as well. Finally we propose a method of approximating the distribution of the maximum order complexity of random sequences. We will then demonstrate how the approximation can be used to estimate the expected value and variance of the maximum order complexity of a random sequence, and the expected value of the number and size of jumps in the maximum order complexity profile. We will show that our approximations of the distribution of the jumps in the pattern counting complexity profile, and the distribution of the maximum order complexity are very close to the true distributions for random sequences.

Automatic generation of the symptom tree model for process fault diagnosis

Abstract: The Symptom Tree Model (STM) has been studied extensively as a model for fault diagnosis in chemical processes and has been applied to real processes. In this study, a program to build a model, AUSST (Automatic Synthesis of the Symptom Tree model), which generates the STM automatically is developed. The input information supplied to AUSST includes the process topology and the unit model library. The unit model library is represented in the form of mini-fault trees which can be constructed systematically through qualitative abstraction from the mathematical model or the operation data and experienced operators. AUSST has worked well, the generated symptom trees describe the paths of fault propagation sufficiently and contain all the possible primal faults. AUSST helps to assure the accuracy of the STM as well as managing the STM consistently. It is expected that AUSST reduces the engineering efforts required to develop a fault diagnostic system for a new process.

Some Hierarchies for the Communication Complexity Measures of Cooperating Grammar Systems

Abstract: We investigate here the descriptional and the computational complexity of parallel communicating grammar systems (PCGS). A new descriptional complexity measure — the communication structure of the PCGS — is introduced and related to the communication complexity (the number of communications). Several hierarchies resulting from these complexity measures and some relations between the measures are established. The results are obtained due to the development of two lower-bound proof techniques for PCGS. The first one is a generalization of pumping lemmas from formal language theory and the second one reduces the lower bound problem for some PCGS to the proof of lower bounds on the number of reversals of certain sequential computing models.

On Some Communication Complexity Problems Related to THreshold Functions

Abstract: We study the computation of threshold functions using formulas over the basis {AND, OR, NOT}, with the aim of unifying the lower bounds of Hansel, Krichevskii, and Khrapchenko For this we consider communication complexity problems related to threshold function computation We obtain an upper bound for the communication complexity problem used by Karchmer and Wigderson to derive the depth version of the lower bound of Khrapchenko This shows that their method, as it is, cannot give better lower bounds We show how better lower bounds can be obtained if the referee (who was ignored in the Karchmer-Wigderson method) is involved in the argument We show that the difficulty of the communication task persists even if the parties are required to operate correctly only for certain special inputs

Some Results on the Complexity of SLD-Derivations

Abstract: In this paper we consider a few simple classes of definite programs and goals and study the problem of deciding whether a given goal has a successful SLD-derivation (the SUCCESS problem). Although the problem is always decidable for the classes studied, it turns out to be NP-complete even for some very simple classes.