133 research outputs found
Boosting-based Construction of BDDs for Linear Threshold Functions and Its Application to Verification of Neural Networks
Understanding the characteristics of neural networks is important but
difficult due to their complex structures and behaviors. Some previous work
proposes to transform neural networks into equivalent Boolean expressions and
apply verification techniques for characteristics of interest. This approach is
promising since rich results of verification techniques for circuits and other
Boolean expressions can be readily applied. The bottleneck is the time
complexity of the transformation. More precisely, (i) each neuron of the
network, i.e., a linear threshold function, is converted to a Binary Decision
Diagram (BDD), and (ii) they are further combined into some final form, such as
Boolean circuits. For a linear threshold function with variables, an
existing method takes time to construct an ordered BDD of
size consistent with some variable ordering. However, it
is non-trivial to choose a variable ordering producing a small BDD among
candidates.
We propose a method to convert a linear threshold function to a specific form
of a BDD based on the boosting approach in the machine learning literature. Our
method takes time and outputs BDD of size
, where is the margin of some
consistent linear threshold function. Our method does not need to search for
good variable orderings and produces a smaller expression when the margin of
the linear threshold function is large. More precisely, our method is based on
our new boosting algorithm, which is of independent interest. We also propose a
method to combine them into the final Boolean expression representing the
neural network
08381 Abstracts Collection -- Computational Complexity of Discrete Problems
From the 14th of September to the 19th of September, the Dagstuhl Seminar
08381 ``Computational Complexity of Discrete Problems\u27\u27 was held in Schloss Dagstuhl - Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work as well as open problems were discussed.
Abstracts of the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this report. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Potential of quantum finite automata with exact acceptance
The potential of the exact quantum information processing is an interesting,
important and intriguing issue. For examples, it has been believed that quantum
tools can provide significant, that is larger than polynomial, advantages in
the case of exact quantum computation only, or mainly, for problems with very
special structures. We will show that this is not the case.
In this paper the potential of quantum finite automata producing outcomes not
only with a (high) probability, but with certainty (so called exactly) is
explored in the context of their uses for solving promise problems and with
respect to the size of automata. It is shown that for solving particular
classes of promise problems, even those without some
very special structure, that succinctness of the exact quantum finite automata
under consideration, with respect to the number of (basis) states, can be very
small (and constant) though it grows proportional to in the case
deterministic finite automata (DFAs) of the same power are used. This is here
demonstrated also for the case that the component languages of the promise
problems solvable by DFAs are non-regular. The method used can be applied in
finding more exact quantum finite automata or quantum algorithms for other
promise problems.Comment: We have improved the presentation of the paper. Accepted to
International Journal of Foundation of Computer Scienc
Complexity classifications for different equivalence and audit problems for Boolean circuits
We study Boolean circuits as a representation of Boolean functions and
consider different equivalence, audit, and enumeration problems. For a number
of restricted sets of gate types (bases) we obtain efficient algorithms, while
for all other gate types we show these problems are at least NP-hard.Comment: 25 pages, 1 figur
From Dust to Dawn: Practically Efficient Two-Party Secure Function Evaluation Protocols and their Modular Design
General two-party Secure Function Evaluation (SFE) allows mutually distrusting parties to (jointly) correctly compute \emph{any} function on their private input data, without revealing the inputs. SFE, properly designed, guarantees to satisfy the most stringent security requirements, even for interactive computation. Two-party SFE can benefit almost any client-server interaction where privacy is required, such as privacy-preserving credit checking, medical classification, or face recognition. Today, SFE is subject of an immense amount of research in a variety of directions, and is not easy to navigate.
In this paper, we systematize the most \emph{practically important} work of the vast research knowledge on \emph{general} SFE. It turns out that the most efficient SFE protocols today are obtained by combining several basic techniques, such as garbled circuits and homomorphic encryption. We limit our detailed discussion to efficient general techniques. In particular, we do not discuss the details of currently \emph{practically inefficient} techniques, such as fully homomorphic encryption (although we elaborate on its practical relevance), nor do we cover \emph{specialized} techniques applicable only to small classes of functions.
As an important practical contribution, we present a framework in which today\u27s practically most efficient techniques for general SFE can be viewed as building blocks with well-defined interfaces that can be easily combined to establish a complete efficient solution. Further, our approach naturally lends itself to automated protocol generation (compilation). This is evidenced by the implementation of (parts of) our framework in the TASTY SFE compiler (introduced at ACM CCS 2010).
In sum, our work is positioned as a comprehensive guide in state-of-the-art SFE, with the additional goal of extracting, systematizing and unifying the most relevant and promising general techniques from among the mass of SFE knowledge. We hope this guide would help developers of SFE libraries and privacy-preserving protocols in selecting the most efficient SFE components available today
Three Modern Roles for Logic in AI
We consider three modern roles for logic in artificial intelligence, which
are based on the theory of tractable Boolean circuits: (1) logic as a basis for
computation, (2) logic for learning from a combination of data and knowledge,
and (3) logic for reasoning about the behavior of machine learning systems.Comment: To be published in PODS 202
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