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.
9465773
Outfix-Free Regular Languages and Prime Outfix-Free Decomposition
A string x is an outfix of a string y if there is a string w such that x1wx2=y, where x = x1x2 and a set X of strings is outfix-free if no string in X is an outfix of any other string in X. We examine the outfix-free regular languages. Based on the properties of outfix strings, we develop a polynomial-time algorithm that determines the outfix-freeness of regular languages. We consider two cases: A language is given as a set of strings and a language is given by an acyclic deterministic finite-state automaton. Furthermore, we investigate the prime outfix-free decomposition of outfix-free regular languages and design a linear-time prime outfix-free decomposition algorithm for outfix-free regular languages. We demonstrate the uniqueness of prime outfix-free decomposition.
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.
18478207
Prefix-Free Regular-Expression Matching
We explore the regular-expression matching problem with respect to prefix-freeness of the pattern. We show that the prefix-free regular expression gives only linear number of matching substrings in the size of a given text. Based on this observation, we propose an efficient algorithm for the prefix-free regular-expression matching problem. Furthermore, we suggest an algorithm to determine whether or not a given regular language is prefix-free.
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.
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.
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.
26807833
Pseudorandom generators and the frequency of simplicity
Allender [2] 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 Kolmogorov-simple strings, then all pseudorandom generators are insecure.
18737987
A Simple Two-Dimensional Coded Detection Scheme in Wireless Sensor Networks
Recently an approach that combined the techniques in distributed classification and the ones in error-correcting codes has been proposed to design a fault-tolerant classification system in wireless networks. The codeword implemented at the fusion center is assigned based on each phenomenon and each detection result of every sensor. A local decision represented by one bit is made according to the codeword and the detection result. Thus, the length of the codeword designed is equal to the number of sensors. In this paper, we propose a new distributed detection scheme combined with two-dimensional channel coding. Multiple detections are conducted by each sensor for the same phenomenon. A two-dimensional code that combines the designed code and a repetition code is implemented at the fusion center for decoding. The virtual code length of this two-dimensional code is the code length of the designed code multiplied with the number of detections conducted at each sensor. Compared with the previous methods, the new scheme has higher classification reliability and lower sensor complexity
16511980
On the Design of Soft-Decision Fusion Rule for Coding Approach in Wireless Sensor Networks
In this work, two soft-decision fusion rules, which are respectively named the maximum a priori (MAP) and the suboptimal minimum Euclidean distance (MED) fusion rules, are designed based on a given employed sensor code and associated local classification. Their performance comparison with the distributed classification fusion using soft-decision decoding (DCSD) proposed in an earlier work is also performed. Simulations show that when the number of faulty sensors is small, the MAP fusion rule remains the best at either low sensor observation signal-to-noise ratios (OSNRs) or low communication channel signal-to-noise ratios (CSNRs), and yet, the DCSD fusion rule gives the best performance at middle to high OSNRs and high CSNRs. However, when the number of faulty sensor nodes grows large, the least complex MED fusion rule outperforms the MAP fusion rule at high OSNRs and high CSNRs.
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.