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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 prove that a pattern basis with certain properties would lead to a useful complexity formula of a specific form, and speculate on how to find such a basis. This formula might take as long to compute on arbitrary functions as a brute-force search among circuits, thus addressing the natural proofs barrier, but has a form amenable to proving lower bounds for well-understood explicit functions.
We introduce a new algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent does not ha
This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine (DTM). Circuit family that emulate DTM are almost all monoton
State complexity of quantum finite automata is one of the interesting topics in studying the power of quantum finite automata. It is therefore of importance to develop general methods how to show state succinctness results for quantum finite automata
We propose a modification to Nielsens circuit complexity for Hamiltonian simulation using the Suzuki-Trotter (ST) method, which provides a network like structure for the quantum circuit. This leads to an optimized gate counting linear in the geodesic
In this article, we investigate various physical implications of quantum circuit complexity using squeezed state formalism of Primordial Gravitational Waves (PGW). Recently quantum information theoretic concepts such as entanglement entropy, and comp