Lower bounds for complexity of finite semigroups

Algorithms and lower bounds in finite automata size complexity

In this thesis we investigate the relative succinctness of several types of finite automata, focusing mainly on the following four basic models: one-way deterministic (1dfas), one-way nondeterministic (1nfas), two-way deterministic (2dfas), and two-way nondeterministic (2nfas). We first establish the exact values of the trade-offs for all conversions from two-way to one-way automata. Specifical...

An Effective Lower Bound for Group Complexity of Finite Semigroups and Automata

The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, Complexity of finite semigroups, Annals of Mathematics (2) 88 (1968), 128–160, motivated by the Prime Decomposition Theorem of K. Krohn and J. Rhodes, Algebraic theory of machines, I: Prime decomposition theorem for finite semigroups and machines, Transactions of the Ameri...

Some Lower Bounds for Estrada Index

Lower complexity bounds for interpolation algorithms

We introduce and discuss a new computational model for Hermite–Lagrange interpolation by nonlinear classes of polynomial interpolants. We distinguish between an interpolation problem and an algorithm that solves it. Our model includes also coalescence phenomena and captures a large variety of known Lagrange-Hermite interpolation problems and algorithms. Like in traditional Hermite–Lagrange inte...

Lower Bounds for Quantum Communication Complexity

We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower bounds developed by Raz [30] to the quantum case. Applying this method we give an exponential separation between bounded error quantum communication complexity a...