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The 3-Satisfiability Problem (3-SAT) is a demanding combinatorial problem, of central importance among the non-deterministic polynomial (NP) complete problems, with applications in circuit design, artificial intelligence and logistics. Even…

In this short note, the author shows that the gap problem of some 3-XOR is NP-hard and can be solved by running Charikar\&Wirth's SDP algorithm for two rounds. To conclude, the author proves that $P=NP$.

The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in…

We provide a parameterized polynomial algorithm for the propositional model counting problem #SAT, the runtime of which is single-exponential in the rank-width of a formula. Previously, analogous algorithms have been known -- e.g.~[Fischer,…

A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the optimal solutions. On the basis of…

Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…

We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…

It is crucial to generate crafted SAT formulas with predefined solutions for the testing and development of SAT solvers since many SAT formulas from real-world applications have solutions. Although some generating algorithms have been…

Many practical applications require solving an optimization over large and high-dimensional data sets, which makes these problems hard to solve and prohibitively time consuming. In this paper, we propose a parallel distributed algorithm…

In this short paper we present a survey of some results concerning the random SAT problems. To elaborate, the Boolean Satisfiability (SAT) Problem refers to the problem of determining whether a given set of $m$ Boolean constraints over $n$…

The (2+p)-Satisfiability (SAT) problem interpolates between different classes of complexity theory and is believed to be of basic interest in understanding the onset of typical case complexity in random combinatorics. In this paper, a…

Ternary quantum systems are being studied because these provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the…

We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…

In this paper, we study an extension of Schoning's algorithm [Schoning, 1991] for 3SAT, the clustered Sparrow algorithm We also present strong arguments that this algorithm is polynomial.

Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while…

The PPSZ algorithm by Paturi, Pudl\'ak, Saks, and Zane [1998] is the fastest known algorithm for Unique k-SAT, where the input formula does not have more than one satisfying assignment. For k>=5 the same bounds hold for general k-SAT. We…

Bender et al. (SPAA 2013) have proposed a theoretical framework for testing in contexts where safety mistakes must be avoided. Testing in such a context is made by machines that need to be often calibrated. Given that calibration costs, it…

Coffman and Sethi proposed a heuristic algorithm, called LD, for multi-processor scheduling, to minimize makespan over flowtime-optimal schedules. LD algorithm is a natural extension of a very well-known list scheduling algorithm, Longest…

In [1] we highlighted the fact that the log polynomial expansion employed in Nature Astron. 3, no.3, 272-277 (2019) [2] is a poor approximation to flat $\Lambda$CDM, so using it to infer deviations from flat $\Lambda$CDM is not…

The paper investigates the computational problem of predicting RNA secondary structures. The general belief is that allowing pseudoknots makes the problem hard. Existing polynomial-time algorithms are heuristic algorithms with no…