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The perfect phylogeny is one of the most used models in different areas of computational biology. In this paper we consider the problem of the Persistent Perfect Phylogeny (referred as P-PP) recently introduced to extend the perfect…

Data Structures and Algorithms · Computer Science 2014-05-30 Paola Bonizzoni , Anna Paola Carrieri , Gianluca Della Vedova , Gabriella Trucco

This paper introduces a new public key cryptosystem based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli) and the discrete logarithm problem. These two hard…

Cryptography and Security · Computer Science 2012-09-25 Abdoul Aziz Ciss , Ahmed Youssef Ould Cheikh , Djiby Sow

The Whitehead Minimization problem is a problem of finding elements of the minimal length in the automorphic orbit of a given element of a free group. The classical algorithm of Whitehead that solves the problem depends exponentially on the…

Group Theory · Mathematics 2007-05-23 A. D. Myasnikov , R. M Haralick

This paper proposes a novel Deep Positive-Negative Prototype (DPNP) model that combines prototype-based learning (PbL) with discriminative methods to improve class compactness and separability in deep neural networks. While PbL…

Machine Learning · Computer Science 2025-01-07 Ramin Zarei-Sabzevar , Ahad Harati

We study solution methods for (strongly-)convex-(strongly)-concave Saddle-Point Problems (SPPs) over networks of two type - master/workers (thus centralized) architectures and meshed (thus decentralized) networks. The local functions at…

Optimization and Control · Mathematics 2022-08-23 Aleksandr Beznosikov , Gesualdo Scutari , Alexander Rogozin , Alexander Gasnikov

In this paper we revisit one of the classical statistical problems, the so-called sparse maximum-likelihood (ML) linear regression. As a way of attacking this type of regression, we present a novel CLuP mechanism that to a degree relies on…

Information Theory · Computer Science 2020-11-24 Mihailo Stojnic

Permutation Pattern Matching (PPM) is the problem of deciding for a given pair of permutations P and T whether the pattern P is contained in the text T. Bose, Buss and Lubiw showed that PPM is NP-complete. In view of this result, it is…

Combinatorics · Mathematics 2020-08-12 Vít Jelínek , Michal Opler , Jakub Pekárek

In our companion paper \cite{Stojnicclupint19} we introduced a powerful mechanism that we referred to as the Controlled Loosening-up (CLuP) for handling MIMO ML-detection problems. It turned out that the algorithm has many remarkable…

Information Theory · Computer Science 2019-09-05 Mihailo Stojnic

Difficulty of calculation of discrete logarithm for any arbitrary Field is the basis for security of several popular cryptographic solutions. Pohlig-Hellman method is a popular choice to calculate discrete logarithm in finite field $F_p^*$.…

Number Theory · Mathematics 2021-04-30 Rajeev Kumar

We study structural aspects of randomized parameterized computation. We introduce a new class ${\sf W[P]}$-${\sf PFPT}$ as a natural parameterized analogue of ${\sf PP}$. Our definition uses the machine based characterization of the…

Computational Complexity · Computer Science 2014-09-30 Ankit Chauhan , B. V. Raghavendra Rao

By analogy with the developed cryptographic theory of discrete logarithm problems, we define several hard problems in Entropoid based cryptography, such as Discrete Entropoid Logarithm Problem (DELP), Computational Entropoid Diffie-Hellman…

Cryptography and Security · Computer Science 2021-04-13 Danilo Gligoroski

Promise Constraint Satisfaction Problems (PCSPs) are a generalization of Constraint Satisfaction Problems (CSPs) where each predicate has a strong and a weak form and given a CSP instance, the objective is to distinguish if the strong form…

Computational Complexity · Computer Science 2023-06-22 Joshua Brakensiek , Venkatesan Guruswami , Sai Sandeep

In this paper, we study a class of fractional semi-infinite polynomial programming (FSIPP) problems, in which the objective is a fraction of a convex polynomial and a concave polynomial, and the constraints consist of infinitely many convex…

Optimization and Control · Mathematics 2021-05-18 Feng Guo , Liguo Jiao

The paper analyzes a new public key cryptosystem whose security is based on a matrix version of the discrete logarithm problem over an elliptic curve. It is shown that the complexity of solving the underlying problem for the proposed system…

Cryptography and Security · Computer Science 2007-05-23 J. J. Climent , E. Gorla , J. Rosenthal

There are a number of results saying that for certain "path-following" algorithms that solve PPAD-complete problems, the solution obtained by the algorithm is PSPACE-complete to compute. We conjecture that these results are special cases of…

Computational Complexity · Computer Science 2015-06-17 Paul W. Goldberg

The aim of this paper is to justify the common cryptographic practice of selecting elliptic curves using their order as the primary criterion. We can formalize this issue by asking whether the discrete log problem (DLOG) has the same…

Number Theory · Mathematics 2016-09-07 David Jao , Stephen D. Miller , Ramarathnam Venkatesan

While the reliable use of some NP-complete problem in tandem with the assumption that P is not equal to NP has eluded cryptographers due to lack of results showing average-case hardness, one alternative which has been explored is reliance…

Cryptography and Security · Computer Science 2017-07-05 Aubrey Alston , Yanrong Wo

Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straight-line programs (SLP), since all algorithms on SLP-generated strings could be applied to processing…

Data Structures and Algorithms · Computer Science 2007-05-23 Yury Lifshits

Recent breakthrough methods \cite{gggz,joux,bgjt} on computing discrete logarithms in small characteristic finite fields share an interesting feature in common with the earlier medium prime function field sieve method \cite{jl}. To solve…

Computational Complexity · Computer Science 2014-02-27 Ming-Deh Huang , Anand Kumar Narayanan

We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than…

Formal Languages and Automata Theory · Computer Science 2014-03-04 Dmitry Chistikov , Rupak Majumdar