Average-case complexity

About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.

Quadratic complexity of binary sequences

Abstract: The linear complexity of a binary sequences is an important attribute in applications such as secure communications. In this article we introduce the concept of quadratic complexity of a binary sequences. It is shown that this complexity measure is closely linked to the theory of primitive Reed-Muller codes. Making use of the parity-check polynomial h(x) of a Reed-Muller code, a new algorithm for the computation of the quadratic complexity profile of a sequence is developed. Experimental results confirm the close resemblance between expected theoretical and practical behaviour.

Linear Complexity and 1-Error Linear Complexity over $F_p$ of M-ary Sidel'nikov Sequences

Abstract: In this paper we derive some lower bounds on the linear complexity and upper bounds on the 1-error linear complexity over of M-ary Sidel'nikov sequences of period when and mod M. In particular, we exactly compute the 1-error linear complexity of ternary Sidel'nikov sequences when and . Based on these bounds we present the asymptotic behavior of the normalized linear complexity and the normalized 1-error linear complexity with respect to the period.

The average time complexity to compute prefix functions in processor networks

Abstract: We analyze the average time complexity of evaluating all prefixes of an input vector over a given algebraic structure . As a computational model networks of finite controls are used and a complexity measure for the average delay of such networks is introduced. Based on this notion, we then define the average case complexity of a computational problem for arbitrary strictly positive input distributions. We give a complete characterization of the average complexity of prefix functions with respect to the underlying algebraic structure resp. the corresponding Moore-machine M. By considering a related reachability problem for finite automata it is shown that the complexity only depends on two properties of M, called confluence and diffluence. We prove optimal lower bounds for the average case complexity. Furthermore, a network design is presented that achieves the optimal delay for all prefix functions and all inputs of a given length while keeping the network size linear. It differs substantially from the known constructions for the worst case.