Related papers: A Reply to "On Salum's Algorithm for X3SAT"
Withdrawn; replaced by longer, more detailed paper quant-ph/0010065.
An exposition of the mathematics underpinning the neural network architecture of a GPT-3-style LLM.
There is no known polynomial-time algorithm that can solve an NP problem. Evolutionary search has been shown to be a viable method of finding acceptable solutions within a reasonable time period. Recently quantum computers have surfaced as…
We provide a simplified proof of the random $k$-XORSAT satisfiability threshold theorem. As an extension we also determine the full rank threshold for sparse random matrices over finite fields with precisely $k$ non-zero entries per row.…
We consider semidefinite programming (SDP) approaches for solving the maximum satisfiability problem (MAX-SAT) and the weighted partial MAX-SAT. It is widely known that SDP is well-suited to approximate the (MAX-)2-SAT. Our work shows the…
We comment on the paper "Teleportation with a uniformly accelerated partner" (quant-ph/0302179).
In this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.
A concise analytical formula is developed for the inverse of an invertible 3 x 3 matrix using a telescoping method, and is generalized to larger square matrices. The formula is confirmed using randomly generated matrices in Matlab
We improve proofs in "The Floyd-Warshall Algorithm, the AP and the TSP (III). We also simplify the method for obtaining a good upper bound for an optimal solution.
This paper has been withdrawn, and is replaced with paper "Solvability of elliptic systems with square integrable boundary data" by the same authors.
This paper has been withdrawn due to an error in the proof of the termination of the algorithm. Moreover, some ideas of this paper are a joint work with John Perry and it is inappropriate to mention only me as an author. John Perry was in…
This paper has been withdrawn by the author(s). Please refer to quant-ph/0311171.
This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
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,…
The paper concerns numerical algorithms for solving the Beltrami equation $f_{\bar{z}}(z)=\mu(z) f_z(z)$ for a compactly supported $\mu$. First, we study an efficient algorithm that has been proposed in the literature, and present its…
The paper has been merged into math/0503283
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…
NP-Complete problems have an important attribute that if one NP-Complete problem can be solved in polynomial time, all NP-Complete problems will have a polynomial solution. The 3-CNF-SAT problem is a NP-Complete problem and the primary…
MaxSAT is an optimization version of the famous NP-complete Satisfiability problem (SAT). Algorithms for MaxSAT mainly include complete solvers and local search incomplete solvers. In many complete solvers, once a better solution is found,…