Zobrazeno 1 - 10
of 975
pro vyhledávání: '"Mukhopadhyay, Partha"'
Let $X=X_1\sqcup X_2\sqcup\ldots\sqcup X_k$ be a partitioned set of variables such that the variables in each part $X_i$ are noncommuting but for any $i\neq j$, the variables $x\in X_i$ commute with the variables $x'\in X_j$. Given as input a square
Externí odkaz:
http://arxiv.org/abs/2404.07986
Black-Box Identity Testing of Noncommutative Rational Formulas in Deterministic Quasipolynomial Time
Rational Identity Testing (RIT) is the decision problem of determining whether or not a noncommutative rational formula computes zero in the free skew field. It admits a deterministic polynomial-time white-box algorithm [Garg, Gurvits, Oliveira, and
Externí odkaz:
http://arxiv.org/abs/2309.15647
Autor:
Mukhopadhyay, Partha
We study lattice wouldsheet theory with continuous time describing free motion of a system of bound string bits. We use a non-local lattice derivative that allows us to preserve all the symmetries of the continuum including the worldsheet local symme
Externí odkaz:
http://arxiv.org/abs/2307.16520
Let $T$ be a matrix whose entries are linear forms over the noncommutative variables $x_1, x_2, \ldots, x_n$. The noncommutative Edmonds' problem (NSINGULAR) aims to determine whether $T$ is invertible in the free skew field generated by $x_1,x_2,\ld
Externí odkaz:
http://arxiv.org/abs/2305.09984
The identity testing of rational formulas (RIT) in the free skew field efficiently reduces to computing the rank of a matrix whose entries are linear polynomials in noncommuting variables\cite{HW15}. This rank computation problem has deterministic po
Externí odkaz:
http://arxiv.org/abs/2209.04797
Hrube\v{s} and Wigderson (2015) initiated the complexity-theoretic study of noncommutative formulas with inverse gates. They introduced the Rational Identity Testing (RIT) problem which is to decide whether a noncommutative rational formula computes
Externí odkaz:
http://arxiv.org/abs/2202.05693
Publikováno v:
Inclusive Developments Through Socio-economic Indicators: New Theoretical and Empirical Insights
We prove two results that shed new light on the monotone complexity of the spanning tree polynomial, a classic polynomial in algebraic complexity and beyond. First, we show that the spanning tree polynomials having $n$ variables and defined over cons
Externí odkaz:
http://arxiv.org/abs/2109.06941
Autor:
Wagner, Josephin, Park, Lauren M., Mukhopadhyay, Partha, Matyas, Csaba, Trojnar, Eszter, Damadzic, Ruslan, Jung, Jeesun, Bell, Andrew S., Mavromatis, Lucas A., Hamandi, Ali M., Rosoff, Daniel B., Vendruscolo, Leandro F., Koob, George F., Pacher, Pal, Lohoff, Falk W.
Publikováno v:
In Brain Behavior and Immunity July 2024 119:494-506
We study \emph{multiplicity equivalence} testing of automata over partially commutative monoids (pc monoids) and show efficient algorithms in special cases, exploiting the structure of the underlying non-commutation graph of the monoid. Specifically,
Externí odkaz:
http://arxiv.org/abs/2002.08633