Somenath Biswas

Somenath Biswas
Indian Institute of Technology Kanpur | IIT Kanpur · Department of Computer Science & Engineering

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38
Publications
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391
Citations

Publications

Publications (38)
Preprint
Full-text available
This paper is a survey of various proofs of the so called {\em fundamental theorem of Markov chains}: every ergodic Markov chain has a unique positive stationary distribution and the chain attains this distribution in the limit independent of the initial distribution the chain started with. As Markov chains are stochastic processes, it is natural t...
Article
This article studies the efficacy of the Metropolis algorithm for the minimum-weight codeword problem . The input is a linear code $C$ given by its generator matrix and our task is to compute a nonzero codeword in the code $C$ of least weight. In particular, we study the Metropolis algorithm on two possible search spaces for the problem: 1) t...
Article
Full-text available
One often needs to turn a coupling $(X_i, Y_i)_{i\geq 0}$ of a Markov chain into a sticky coupling where once $X_T = Y_T$ at some $T$, then from then on, at each subsequent time step $T'\geq T$, we shall have $X_{T'} = Y_{T'}$. However, not all of what are considered couplings in literature, even Markovian couplings, can be turned into sticky coupl...
Article
We study the performance of the Metropolis algorithm for the problem of finding a code word of weight less than or equal to M, given a generator matrix of an [n; κ]-binary linear code. The algorithm uses the set Sκ of all κ × κ invertible matrices as its search space where two elements are considered adjacent if one can be obtained from the other v...
Article
In order to understand what makes natural proteins fold rapidly, Šali, Shakhnovich and Karplus (1994) and had used the Metropolis algorithm to search for the minimum energy conformations of chains of beads in the lattice model of protein folding. Based on their computational experiments, they concluded that the Metropolis algorithm would find the m...
Conference Paper
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In this paper we study the suitability of the Metropolis Algorithm and its generalization for solving the shortest lattice vector problem (SVP). SVP has numerous applications spanning from robotics to computational number theory, viz., polynomial factorization. At the same time, SVP is a notoriously hard problem. Not only it is NP-hard, there is no...
Article
In this paper edge-deletion problems are studied with a new perspective. In general an edge-deletion problem is of the form: Given a graph G, does it have a subgraph H obtained by deleting zero or more edges such that H satisfies a polynomial-time verifiable property? This paper restricts attention to first-order expressible properties. If the prop...
Conference Paper
Full-text available
This paper focusses on the performance of the Metropolis algorithm when employed for solving combinatorial optimization problems. One finds in the literature two notions of success for the Metropolis algorithm in the context of such problems. First, we show that both these notions are equivalent. Next, we provide two characterizations, or in other...
Article
Full-text available
Runtime analysis of evolutionary algorithms has become an important part in the theoretical analysis of randomized search heuristics. The first combinatorial problem where rigorous runtime results have been achieved is the well-known single source shortest path (SSSP) problem. Scharnow, Tinnefeld and Wegener [PPSN 2002, J. Math. Model. Alg. 2004] p...
Article
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We show in this paper that the BGS model of abstract state machines can be simulated by random access machines with at most a polynomial time overhead. This result is already stated in [5] with a very brief proof sketch. The present paper gives a detailed proof of the result. We represent hereditarily finite sets, which are the typical BGS ASM obje...
Article
Full-text available
Prediction of fold from amino acid sequence of a protein has been an active area of research in the past few years, but the limited accuracy of existing techniques emphasizes the need to develop newer approaches to tackle this task. In this study, we use contact map prediction as an intermediate step in fold prediction from sequence. Contact map is...
Conference Paper
Full-text available
The complexity of gene regulatory network models stems from the fact that the models should be able to represent continuous, dis- crete as well as stochastic aspects of gene regulation. Hybrid stochastic Petri nets are the models, which can fairly incorporate all these aspects while keeping the model as simple as possible for biologists. This paper...
Article
Full-text available
We give a simple and new randomized primality testing algorithm by reducing primality testing for number n to testing if a specific univariate identity over Zn holds. We also give new randomized algorithms for testing if a multivariate polynomial, over a finite field or over rationals, is identically zero. The first of these algorithms also works o...
Article
Full-text available
The problem of identifying the common three-dimensional structure between two protein molecules has received considerable attention from both the biology community and also from algorithms researchers. A number of similarity measures have been proposed so far for this purpose. Among them are the RMS distance, those based on geometric hashing, and s...
Conference Paper
Gives a simple and new primality testing algorithm by reducing primality testing for a number n to testing if a specific univariate identity over Z<sub>n</sub> holds. We also give new randomized algorithms for testing if a multivariate polynomial, over a finite field or over rationals, is identically zero. The first of these algorithms also works o...
Conference Paper
Identifying the common 3-D substructure between two drug or protein molecules is an important problem in synthetic drug design and molecular biology. This problem can be represented as the following geometric pattern matching problem: given two point sets A and B in three-dimensions, and a real number∈ > 0, find the maximum cardinality subset S ⊆ S...
Article
Abstract Let C be any complexity class closed under log-lin reductions. We show that all sets complete for C under 1-L reductions are polynomialtime isomorphic to each other. We also generalize the result to reductions computed by finite-crossing machines. As a corollary, we show that all sets complete for C under 2-way DFA reductions are polynomia...
Article
Full-text available
We obtain a new definition of creativeness for NP, called NP-creativeness. We show that all NP-creative sets are NP-complete and provide strong evidence that all known NP-complete sets are NP-creative. We also show that all NP-creative sets are complete under exponentially honest reductions and contain an infinite NP subset in their complement (in...
Conference Paper
Let C be any complexity class closed under log-lin reductions. It is shown that all complete sets for C under 1-L reductions are polynomial time isomorphic to one other. It is indicated how to generalize the result to reductions computed by finite-crossing machines
Conference Paper
Full-text available
Two operators, join and equivalence, are defined on R , a polynomial-time verifiable binary relation witnessing language A in NP. It is proved that if R has these two operators and there is an instance of A with certain specific properties, then A is NP-complete. Relations with the above properties are called universal relations. It is shown that i...
Article
A new property of NP sets called commitability is introduced. Roughly, a language ℒ in NP is commitable if given any instance x, and any string y, a string z can be found in polynomial time such that z is in L iff y is a prefix of a witness of x in the context of a PTIME relation that defines ℒ. It is shown that all NP sets complete under polynomia...
Book
This volume contains the proceedings of the Eleventh Conference on Foundations of Software Technology and Theoretical Computer Science held in New Dehli, India December 17-19, 1991. Three invited papers and 25 contributed papers selected from 78 submissions by authors from many different countries reflect the current research concerns of the theore...
Article
In the present paper we study the complexity of some restricted versions of the satisfiability problem for propositional CNF formulas. We define these restrictions through their corresponding languages which are identified using the self-reducibility property of satisfiable propositional CNF formulas. The notion of kernel constructibility (similar...
Article
To detect errors in decision tables one needs to decide whether a given set of constraints is feasible or not. This paper describes an algorithm to do so when the constraints are linear in variables that take only integer values. Decision tables with such constraints occur frequently in business data processing and in nonnumeric applications. The a...
Article
There are, essentially, just 17 subsets of the 16 binary logical operations which are both (a) complete in the sense that any n-variable logical function can be expressed with them and (b) minimal, subject to (a). For each of these bases, it is shown ...
Article
This paper deals with certain characterizations of the sets of positive integers which when represented as strings on a finite alphabet, form tree adjunct languages, As the context free languages constitute a subfamily of tree adjunct languages, the results carry over to the former as well.
Article
Full-text available
Almost all functions of a living organism at its cellular level are carried out through various classes of proteins. Our body consists of many kinds of cells, and each cell carries a copy of the genome– which is the program which a cell executes for its functioning. The genome is a polymer, or a chain; for us, it is a sequence of four kinds of mole...

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