Peter Gacs showed [1] that for every n there exists a bit string x of length n whose plain complexity C (x) has almost maximal conditional complexity relative to x, i.e., C (C (x)|x) ≥ log n− log n−O(1). Here log(i) = log log i etc. Following Elena Kalinina [3], we provide a gametheoretic proof of this result; modifying her argument, we get a better (and tight) bound log n − O(1). We also show ...

This paper presents a novel split-radix fast Fourier transform (SRFFT) pipeline architecture design. A mapping methodology has been developed to obtain regular and modular pipeline for split-radix algorithm. The pipeline is repartitioned to balance the latency between complex multiplication and butterfly operation by using carry-save addition. The number of complex multiplier is minimized via a...

Directed Acyclic Graphs are often used to model circuits and networks. The path length in such Directed Acyclic Graphs represents circuit or network delays. In the vertex splitting problem, the objective is to determine a minimum number of vertices from the graph to split such that the resulting graph has no path of length greater than a given δ. The problem has been proven to be NP-hard. A Gen...

The problem of computing the length of the maximal common subsequences of two strings is quite well examined in the sequential case. There are many variations, but the standard approach is to compute the length in quadratic time using dynamic programming. A lineartime parallel algorithm can be obtained via a simple modification of this strategy by letting a linear number of processors sweep thr...

The compact directed acyclic word graph (CDAWG) of a string T of length n takes space proportional just to the number e of right extensions of the maximal repeats of T , and it is thus an appealing index for highly repetitive datasets, like collections of genomes from similar species, in which e grows significantly more slowly than n. We reduce from O(m log log n) to O(m) the time needed to cou...

A k-bit Hamming prefix code is a binary code with the following property: for any codeword x and any prefix y of another codeword, both x and y having the same length, the Hamming distance between x and y is at least k. Given an alphabet A = [a1, . . . , an] with corresponding probabilities [p1, . . . , pn], the k-bit Hamming prefix code problem is to find a k-bit Hamming prefix code for A with...

Multivariate Poisson approximation of the length spectrum of random surfaces is studied by means of the Chen-Stein method. This approach delivers simple and explicit error bounds in Poisson limit theorems. They are used to prove that Poisson approximation applies to curves of length up to order o(log log g) with g being the genus of the surface.

We study homomorphic hash functions into SL2(q), the 2 × 2 matrices with determinant 1 over the field with q elements. Modulo a well supported number theoretic hypothesis, which holds in particular for all concrete homomorphisms proposed thus far, we prove that a random homomorphism is at least as secure as any concrete homomorphism. For a family of homomorphisms containing several concrete pro...

The dynamic trie is a fundamental data structure which finds applications in many areas. This paper proposes a compressed version of the dynamic trie data structure. Our data-structure is not only space efficient, it also allows pattern searching in o(|P |) time and leaf insertion/deletion in o(log n) time, where |P | is the length of the pattern and n is the size of the trie. To demonstrate th...

It’s easy to check that any specific string of length n has probability at most (1 − δ), hence SV-sources are n log 1 1−δ -sources. Also recall that SV-sources are (k, l) block sources where k = l log 1 1−δ . Suppose δ = log 1 1−δ , then k = δl. Take a hash-based extractor E : {0, 1} × {0, 1} → {0, 1}. Here, our weak-source is a SVsource over the strings of length n and suppose k = n log 1 1−δ ...