14156578
Shorter Regular Expressions from Finite-State Automata
We consider the use of state elimination to construct shorter regular expressions from finite-state automata. Although state elimination is an intuitive method for computing regular expressions from finite-state automata, the resulting regular expressions are often very long and complicated. We examine the minimization of finite-state automata to obtain shorter expressions first. Then, we introduce vertical chopping based on bridge states and horizontal chopping based on the structural properties of given finite-state automata. We prove that we should not eliminate bridge states until we eliminate all non-bridge states to obtain shorter regular expressions. In addition, we suggest heuristics for state elimination that lead to shorter regular expressions based on vertical chopping and horizontal chopping. 
 
Note that we have omitted almost all proofs in this preliminary version.
8774753
Overlap-Free Regular Languages
We define a language to be overlap-free if any two distinct strings in the language do not overlap with each other. We observe that overlap-free languages are a proper subfamily of infix-free languages and also a proper subfamily of comma-free languages. Based on these observations, we design a polynomial-time algorithm that determines overlap-freeness of a regular language. We consider two cases: A language is specified by a nondeterministic finite-state automaton and a language is described by a regular expression. Furthermore, we examine the prime overlap-free decomposition of overlap-free regular languages and show that the prime overlap-free decomposition is not unique.
33469096
The generalization of generalized automata: expression automata
We explore expression automata with respect to determinism and minimization. We define determinism of expression automata using prefix-freeness. This approach is, to some extent, similar to that of Giammarresi and Montalbano's definition of deterministic generalized automata. We prove that deterministic expression automata languages are a proper subfamily of the regular languages. We close by defining the minimization of deterministic expression automata.
10385992
A New Linearizing Restriction in the Pattern Matching Problem
In the pattern matching problem, there can be a quadratic number of matching substrings in the size of a given text. The linearizing restriction finds, at most, a linear number of matching substrings. We first explore two well-known linearizing restriction rules, the longest-match rule and the shortest-match substring searchrule, and show that both rules give the same result when a pattern is an infix-free set even though they have different semantics. Then, we introduce a new linearizing restriction, the leftmost non-overlapping match rule that is suitable for find-and-replace operations in text searching, and propose an efficient algorithm when the pattern is a regular language according to the new match rule.
14544092
Intercode Regular Languages
Intercodes are a generalization of comma-free codes. Using the structural properties of finite-state automata recognizing an intercode we develop a polynomial-time algorithm for determining whether or not a given regular language L is an intercode. If the answer is yes, our algorithm yields also the smallest index k such that L is a k-intercode. 
 
Furthermore, we examine the prime intercode decomposition of intercode regular languages and design an algorithm for the intercode primality test of an intercode recognized by a finite-state automaton. We also propose an algorithm that computes the prime intercode decomposition of an intercode regular language in polynomial time. Finally, we demonstrate that the prime intercode decomposition need not be unique.
1251651
Obtaining shorter regular expressions from finite-state automata
We consider the use of state elimination to construct shorter regular expressions from finite-state automata (FAs). Although state elimination is an intuitive method for computing regular expressions from FAs, the resulting regular expressions are often very long and complicated. We examine the minimization of FAs to obtain shorter expressions first. Then, we introduce vertical chopping based on bridge states and horizontal chopping based on the structural properties of given FAs. We prove that we should not eliminate bridge states until we eliminate all non-bridge states to obtain shorter regular expressions. In addition, we suggest heuristics for state elimination that leads to shorter regular expressions based on vertical chopping and horizontal chopping.
32557120
Pseudorandom Generators and the Frequency of Simplicity
Allender [All89] showed that if there are dense P languages containing only a finite set of Kolmogorov-simple strings, then all pseudorandom generators are insecure. We extend this by proving that if there are dense P (or even BPP) languages containing only a sparse set of Kolmogorovsimple strings, then all pseudorandom generators are insecure.
2350989
Privacy-Preserving Multivariate Statistical Analysis: Linear Regression and Classification
Multivariate statistical analysis is an important data analysis technique that has found applications in various areas. In this paper, we study some multivariate statistical analysis methods in Secure 2-party Computation (S2C) framework illustrated by the following scenario: two parties, each having a secret data set, want to conduct the statistical analysis on their joint data, but neither party is willing to disclose its private data to the other party or any third party. The current statistical analysis techniques cannot be used directly to support this kind of computation because they require all parties to send the necessary data to a central place. In this paper, We define two Secure 2-party multivariate statistical analysis problems: Secure 2-party Multivariate Linear Regression problem and Secure 2-party Multivariate Classification problem. We have developed a practical security model, based on which we have developed a number of building blocks for solving these two problems.
9252244
A pairwise key pre-distribution scheme for wireless sensor networks
To achieve security in wireless sensor networks, it is important to be able to encrypt and authenticate messages sent among sensor nodes. Keys for encryption and authentication purposes must be agreed upon by communicating nodes. Due to resource constraints, achieving such key agreement in wireless sensor networks is non-trivial. Many key agreement schemes used in general networks, such as Diffie-Hellman and public-key based schemes, are not suitable for wireless sensor networks. Pre-distribution of secret keys for all pairs of nodes is not viable due to the large amount of memory used when the network size is large. To solve the key pre-distribution problem, two elegant key pre-distribution approaches have been proposed recently [11, 7].In this paper, we propose a new key pre-distribution scheme, which substantially improves the resilience of the network compared to the existing schemes. Our scheme exhibits a nice threshold property: when the number of compromised nodes is less than the threshold, the probability that any nodes other than these compromised nodes is affected is close to zero. This desirable property lowers the initial payoff of smaller scale network breaches to an adversary, and makes it necessary for the adversary to attack a significant proportion of the network. We also present an in depth analysis of our scheme in terms of network resilience and associated overhead.
18991175
Performance Analysis and Code Design for Minimum Hamming Distance Fusion in Wireless Sensor Networks
Distributed classification fusion using error-correcting codes (DCFECC) has recently been proposed for wireless sensor networks operating in a harsh environment. It has been shown to have a considerably better capability against unexpected sensor faults than the optimal likelihood fusion. In this paper, we analyze the performance of a DCFECC code with minimum Hamming distance fusion. No assumption on identical distribution for local observations, as well as common marginal distribution for the additive noises of the wireless links, is made. In addition, sensors are allowed to employ their own local classification rules. Upper bounds on the probability of error that are valid for any finite number of sensors are derived based on large deviations technique. A necessary and sufficient condition under which the minimum Hamming distance fusion error vanishes as the number of sensors tends to infinity is also established. With the necessary and sufficient condition and the upper error bounds, the relation between the fault-tolerance capability of a DCFECC code and its pair-wise Hamming distances is characterized, and can be used together with any code search criterion in finding the code with the desired fault-tolerance capability. Based on the above results, we further propose a code search criterion of much less complexity than the minimum Hamming distance fusion error criterion adopted earlier by the authors. This makes the code construction with acceptable fault-tolerance capability for a network with over a hundred of sensors practical. Simulation results show that the code determined based on the new criterion of much less complexity performs almost identically to the best code that minimizes the minimum Hamming distance fusion error. Also simulated and discussed are the performance trends of the codes searched based on the new simpler criterion with respect to the network size and the number of hypotheses
46047704
A New Decoding Algorithm for Complete Decoding of Linear Block Codes
In this paper we present and describe an improved version of the Zero-Neighbors algorithm, which we call the Zero-Coverings algorithm. We also present a method for finding a smallest subset of codewords ( Zero-Coverings) which need to be stored to perform the Zero-Coverings algorithm. For some short codes, the sizes of Zero-Coverings are obtained by computer searches; for long codes, an asymptotic bound on the sizes of such subsets is also given.