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.
8730288
On the existence of prime decompositions
We investigate factorizations of regular languages in terms of prime languages. A language is said to be strongly prime decomposable if any way of factorizing it yields a prime decomposition in a finite number of steps. We give a characterization of the strongly prime decomposable regular languages and using the characterization we show that every regular language over a unary alphabet has a prime decomposition. We show that there exist non-regular unary languages that do not have prime decompositions. We also consider infinite factorizations of unary languages.
8761097
Prime Decompositions of Regular Languages
We investigate factorizations of regular languages in terms of prime languages. A language is said to be strongly prime decomposable if any way of factorizing the language yields a prime decomposition in a finite number of steps. We give a characterization of the strongly prime decomposable regular languages and using the characterization we show that every regular language over a unary alphabet has a prime decomposition. We show that there exist co-context-free languages that do not have prime decompositions.
38202538
Infix-free Regular Expressions and Languages
We study infix-free regular languages. We observe the structural properties of finite-state automata for infix-free languages and develop a polynomial-time algorithm to determine infix-freeness of ...
1671028
A key management scheme for wireless sensor networks using deployment knowledge
To achieve security in wireless sensor networks, it is important to he able to encrypt messages sent among sensor nodes. Keys for encryption purposes must he agreed upon by communicating nodes. Due to resource constraints, achieving such key agreement in wireless sensor networks is nontrivial. 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. Recently, a random key pre-distribution scheme and its improvements have been proposed. A common assumption made by these random key pre-distribution schemes is that no deployment knowledge is available. Noticing that in many practical scenarios, certain deployment knowledge may be available a priori, we propose a novel random key pre-distribution scheme that exploits deployment knowledge and avoids unnecessary key assignments. We show that the performance (including connectivity, memory usage, and network resilience against node capture) of sensor networks can he substantially improved with the use of our proposed scheme. The scheme and its detailed performance evaluation are presented in this paper.
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.
11579937
Using MDS Codes for the Key Establishment of Wireless Sensor Networks
Key pre-distribution techniques for security provision of Wireless Sensor Networks (WSNs) have attracted significant interests recently. In these schemes, a relatively small number of keys are randomly chosen from a large key pool and loaded on the sensors prior to deployment. After being deployed, each sensor tries to find a common key shared by itself and each of its neighbors to establish a link key to protect the wireless communication between themselves. One intrinsic disadvantage of such techniques is that some neighboring sensors do not share any common key. In order to establish a link key among such neighbors, a multi-hop secure path may be used to deliver the secret. Unfortunately, the possibility of sensors being compromised on the path may render such establishment process insecure. 
 
In this work, we propose and analyze an Incremental Redundancy Transmission (IRT) scheme that uses the powerful Maximum Distance Separable (MDS) codes to address the problem. In the IRT scheme, the encoded secret link key is transmitted through multiple multi-hop paths. To reduce the total information that needs to be transmitted, the redundant symbols of the MDS codes are transmitted only if the destination fails to decode the secret. One salient feature of the IRT scheme is the flexibility of trading transmission for lower information disclosure. Theoretical and simulation results are presented to support our claim.
10524443
Distance-spectrum formulas on the largest minimum distance of block codes
A general formula for the asymptotic largest minimum distance (in block length) of deterministic block codes under generalized distance functions (not necessarily additive, symmetric, and bounded) is presented. As revealed in the formula, the largest minimum distance can be fully determined by the ultimate statistical characteristics of the normalized distance function evaluated under a properly chosen random-code generating distribution. Interestingly, the new formula has an analogous form to the general information-spectrum expressions of the channel capacity and the optimistic channel capacity, respectively derived by Verdu and Han (1994) and Chen and Alajaji (1998, 1999). As a result, a minor class of distance functions for which the largest minimum distance can be derived is characterized. A general Varshamov-Gilbert lower bound is next addressed. Some discussions on the tightness of the general Varshamov-Gilbert bound are also provided. Finally, lower bounds on the largest minimum distances for several specific block coding schemes are rederived in terms of the new formulas, followed by comparisons with the known results devoted to the same codes.
6196244
Decoding Linear Block Codes Using a Priority-First Search : Performance Analysis and Suboptimal Version
An efficient maximum-likelihood soft-decision decoding algorithm for linear block codes using a generalized Dijkstra's algorithm was proposed by Han, Hartmann, and Chen (1993). We prove that this algorithm is efficient for most practical communication systems where the probability of error is less than 10/sup -3/ by finding an upper bound of the computational effort of the algorithm. A suboptimal decoding algorithm is also proposed. The performance of this suboptimal decoding algorithm is within 0.25 dB of the performance of an optimal decoding algorithm for the (104, 52) binary extended quadratic residue code, and within 0.5 dB of the optimal performance for the (128, 64) binary BCH code, respectively.