Related papers: Polymorphisms and Circuit Complexity
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be…
It is already shown that a Boolean function for a NP-complete problem can be computed by a polynomial-sized circuit if its variables have enough number of automorphisms. Looking at this previous study from the different perspective gives us…
Complexity theory offers a variety of concise computational models for computing boolean functions - branching programs, circuits, decision trees and ordered binary decision diagrams to name a few. A natural question that arises in this…
In pursuit of a deeper understanding of Boolean Promise Constraint Satisfaction Problems (PCSPs), we identify a class of problems with restricted structural complexity, which could serve as a promising candidate for complete…
We discuss ways in which tools from topology can be used to derive lower bounds for the circuit complexity of Boolean functions.
Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…
We describe and motivate a proposed new approach to lowerbounding the circuit complexity of boolean functions, based on a new formalization of "patterns" as elements of a special basis of the vector space of all truth table properties. We…
The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…
Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…
We study Boolean circuits as a representation of Boolean functions and consider different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all…
We study the computational complexity of two Boolean nonlinearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time…
Quantum circuit complexity has played a central role in recent advances in holography and many-body physics. Within quantum field theory, it has typically been studied in a Lorentzian (real-time) framework. In a departure from standard…
We study the circuit complexity of boolean functions in a certain infinite basis. The basis consists of all functions that take value $1$ on antichains over the boolean cube. We prove that the circuit complexity of the parity function and…
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Boolean nested canalizing functions (NCFs) have important applications in molecular regulatory networks, engineering and computer science. In this paper, we study their certificate complexity. For both Boolean values $b\in\{0,1\}$, we…
Boolean nested canalizing functions (NCFs) have important applications in molecular regulatory networks, engineering and computer science. In this paper, we study their certificate complexity. For both Boolean values $b\in\{0,1\}$, we…
Cyclic and non-wellfounded proofs are now increasingly employed to establish metalogical results in a variety of settings, in particular for type systems with forms of (co)induction. Under the Curry-Howard correspondence, a cyclic proof can…
This was submitted as a final project for CS254B, taught by Li Yang Tan and Tom Knowles. The field of Circuit Complexity utilises careful analysis of Boolean Circuit Functions in order to extract meaningful information about a range of…