Related papers: Boolean Matching Reversible Circuits: Algorithm an…
Provably correct software is one of the key challenges of our software-driven society. Program synthesis -- the task of constructing a program satisfying a given specification -- is one strategy for achieving this. The result of this task…
Quantum circuit mapping is a crucial process in the quantum circuit compilation pipeline, facilitating the transformation of a logical quantum circuit into a list of instructions directly executable on a target quantum system. Recent…
Basic multimode impedance analysis grounded in the availability of nonequilibrium charge carriers and their retarded path towards equilibrium is used to access the inadequacy of equivalent circuits in nonlinear systems with inherent memory.…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
In this paper, reversible circuits consisting of NOT, CNOT and 2-CNOT gates are studied. Several asymptotically optimal by the order of magnitude synthesis methods are described. Some circuit's complexity reduction approaches are…
The problem of constructing hazard-free Boolean circuits dates back to the 1940s and is an important problem in circuit design. Our main lower-bound result unconditionally shows the existence of functions whose circuit complexity is…
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
In this paper, we present a novel algorithm to solve the Boolean Satisfiability (SAT) problem, using noise-based logic (NBL). Contrary to what the name may suggest, NBL is not a random/fuzzy logic system. In fact, it is a completely…
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…
The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is epsilon-far from having that property. The performance of the algorithm is judged by how many calls need to be made to…
Reactive synthesis aims at automatic construction of systems from their behavioural specifications. The research mostly focuses on synthesis of systems dealing with Boolean signals. But real-life systems are often described using…
Realizing a conceptual quantum algorithm on an actual physical device necessitates the algorithm's quantum circuit description to undergo certain transformations in order to adhere to all constraints imposed by the hardware. In this regard,…
The general adversary dual is a powerful tool in quantum computing because it gives a query-optimal bounded-error quantum algorithm for deciding any Boolean function. Unfortunately, the algorithm uses linear qubits in the worst case, and…
Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…
In this paper, a new non-search based synthesis algorithm for reversible circuits is proposed. Compared with the widely used search-based methods, our algorithm is guarantied to produce a result and can lead to a solution with much fewer…
The use of Boolean Satisfiability (SAT) solver for hardware verification incurs exponential run-time in several instances. In this work we have proposed an efficient quantum SAT (qSAT) solver for equivalence checking of Boolean circuits…
We define a formal framework for equivalence checking of sequential quantum circuits. The model we adopt is a quantum state machine, which is a natural quantum generalisation of Mealy machines. A major difficulty in checking quantum…
We provide a polynomial time reduction from Bayesian incentive compatible mechanism design to Bayesian algorithm design for welfare maximization problems. Unlike prior results, our reduction achieves exact incentive compatibility for…
The paper discusses various applications of permutation group theory in the synthesis of reversible logic circuits consisting of Toffoli gates with negative control lines. An asymptotically optimal synthesis algorithm for circuits…