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Boolean satisfiability is a propositional logic problem of interest in multiple fields, e.g., physics, mathematics, and computer science. Beyond a field of research, instances of the SAT problem, as it is known, require efficient solution…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
In complexity theory, there exists a famous unsolved problem whether NP can be P or not. In this paper, we discuss this aspect in SAT (satisfiability) problem, and it is shown that the SAT can be solved in plynomial time by means of quantum…
The utility of satisfiability (SAT) as an application focused hard computational problem is well established. We explore the potential of quantum annealing to enhance classical SAT solving, especially where sampling from the space of all…
Boolean satisfiability (SAT) solving is a fundamental problem in computer science. Finding efficient algorithms for SAT solving has broad implications in many areas of computer science and beyond. Quantum SAT solvers have been proposed in…
What is the power of polynomial-time quantum computation with access to an NP oracle? In this work, we focus on two fundamental tasks from the study of Boolean satisfiability (SAT) problems: search-to-decision reductions, and approximate…
In this paper we propose the approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm…
The question of whether or not quantum computers can efficiently solve NP-complete problems is open, although indications are that BQP does not contain NP. Still, many of these problems are natural candidates for solution on quantum…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
The problem of P vs. NP is very serious, and solutions to the problem can help save lives. This article is an attempt at solving the problem using a computer algorithm. It is presented in a fashion that will hopefully allow for easy…
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…
Quantum computers have the potential of solving problems more efficiently than classical computers. While first commercial prototypes have become available, the performance of such machines in practical application is still subject to…
A new quantum algorithm is proposed to solve Satisfiability(SAT) problems by taking advantage of non-unitary transformation in ground state quantum computer. The energy gap scale of the ground state quantum computer is analyzed for 3-bit…
Efficient solutions to NP-complete problems would significantly benefit both science and industry. However, such problems are intractable on digital computers based on the von Neumann architecture, thus creating the need for alternative…
The question of whether the complexity class P is equal to the complexity class NP has been a seemingly intractable problem for over 4 decades. It has been clear that if an algorithm existed that would solve the problems in the NP class in…
A computer which has access to a closed timelike curve, and can thereby send the results of calculations into its own past, can exploit this to solve difficult computational problems efficiently. I give a specific demonstration of this for…
NP complete problem is one of the most challenging issues. The question of whether all problems in NP are also in P is generally considered one of the most important open questions in mathematics and theoretical computer science as it has…
Recently a great deal of attention has focused on quantum computation following a sequence of results suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor's result that factoring and the…