Related papers: On the Applicability of Post's Lattice
Proving complexity lower bounds remains a challenging task: we only know how to prove conditional uniform lower bounds and nonuniform lower bounds in restricted circuit models. Williams (STOC 2010) showed how to derive nonuniform lower…
Polynomial threshold gates are basic processing units of an artificial neural network. When the input vectors are binary vectors, these gates correspond to Boolean functions and can be analyzed via their polynomial representations. In…
Let A be a finite set with at least two elements. The composition of two classes I and J of operations on A, is defined as the set of all compositions of functions in I with functions in J. This binary operation gives a monoid structure to…
The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to…
A linear constraint loop is specified by a system of linear inequalities that define the relation between the values of the program variables before and after a single execution of the loop body. In this paper we consider the problem of…
For $A\in\mathbb{Z}^{m\times n}$ we investigate the behaviour of the number of lattice points in $P_A(b)=\{x\in\mathbb{R}^n:Ax\leq b\}$, depending on the varying vector $b$. It is known that this number, restricted to a cone of constant…
This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…
Comparator circuit model was originally introduced by Mayr and Subramanian (1992) (and further studied by Cook, Filmus and Le (2012)) to capture problems which are not known to be P-complete but still not known to admit efficient parallel…
Boolean cardinality constraints state that at most (at least, or exactly) $k$ out of $n$ propositional literals can be true. We propose a new class of selection networks that can be used for an efficient encoding of them. Several comparator…
The study of various decision problems for logic fragments has a long history in computer science. This paper is on the membership problem for a fragment of first-order logic over infinite words; the membership problem asks for a given…
The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum…
This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…
Let $P$ be a partially ordered set. We prove that if $n$ is sufficiently large, then there exists a packing $\mathcal{P}$ of copies of $P$ in the Boolean lattice $(2^{[n]},\subset)$ that covers almost every element of $2^{[n]}$:…
We study how linear orders can be employed to realise choice functions for which the set of potential choices is restricted, i.e., the possible choice is not possible among the full powerset of all alternatives. In such restricted settings,…
We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as…
Finding whether a linear-constraint loop has a linear ranking function is an important key to understanding the loop behavior, proving its termination and establishing iteration bounds. If no preconditions are provided, the decision problem…
This paper presents a method for computing a least fixpoint of a system of equations over booleans. The resulting computation can be significantly shorter than the result of iteratively evaluating the entire system until a fixpoint is…
Arithmetic circuits (AC) are circuits over the real numbers with 0/1-valued input variables whose gates compute the sum or the product of their inputs. Positive AC -- that is, AC representing non-negative functions -- subsume many…
In this paper, we study the structure of set-multilinear arithmetic circuits and set-multilinear branching programs with the aim of showing lower bound results. We define some natural restrictions of these models for which we are able to…
We say that a circuit $C$ over a field $F$ functionally computes an $n$-variate polynomial $P$ if for every $x \in \{0,1\}^n$ we have that $C(x) = P(x)$. This is in contrast to syntactically computing $P$, when $C \equiv P$ as formal…