Related papers: An elementary proof of the halting property for Ch…
In this paper we study for a given azimuthal quantum number $\kappa$ the eigenvalues of the Chandrasekhar-Page angular equation with respect to the parameters $\mu:=am$ and $\nu:=a\omega$, where $a$ is the angular momentum per unit mass of…
We revisit a technique of S. Lehr on automata and use it to prove old and new results in a simple way. We give a very simple proof of the 1986 theorem of Honkala that it is decidable whether a given k-automatic sequence is ultimately…
Although the halting problem is undecidable, imperfect testers that fail on some instances are possible. Such instances are called hard for the tester. One variant of imperfect testers replies "I don't know" on hard instances, another…
The motivation and construction of the original Quenched Eguchi-Kawai model are reviewed, providing much greater detail than in the first, 1982 QEK paper. A 2008 article announced that QEK fails as a reduced model because the average over…
Havel in 1955, Erd\H{o}s and Gallai in 1960, Hakimi in 1962, Ruskey, Cohen, Eades and Scott in 1994, Barnes and Savage in 1997, Kohnert in 2004, Tripathi, Venugopalan and West in 2010 proposed a method to decide, whether a sequence of…
The conjecture by Steklov was solved negatively by Rakhmanov in 1979. His original proof was based on the formula for orthogonal polynomial obtained by adding point masses to the measure of orthogonality. In this note, we show how this…
The Turing machine halting problem can be explained by several factors, including arithmetic logic irreversibility and memory erasure, which contribute to computational uncertainty due to information loss during computation. Essentially,…
A popular method for finding the projection onto the intersection of two closed convex subsets in Hilbert space is Dykstra's algorithm. In this paper, we provide sufficient conditions for Dykstra's algorithm to converge rapidly, in finitely…
Accelerator design languages (ADLs), high-level languages that compile to hardware units, help domain experts quickly design efficient application-specific hardware. ADL compilers optimize datapaths and convert software-like control flow…
The Kaczmarz algorithm (KA) is a popular method for solving a system of linear equations. In this note we derive a new exponential convergence result for the KA. The key allowing us to establish the new result is to rewrite the KA in such a…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
The chiral Potts model continues to pose particular challenges in statistical mechanics: it is ``exactly solvable'' in the sense that it satisfies the Yang-Baxter relation, but actually obtaining the solution is not easy. Its free energy…
We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer.…
Approximate proof labeling schemes were introduced by \\Censor-Hillel, Paz and Perry \cite{CPP}. Roughly speaking, a graph property~$\cP$ can be verified by an approximate proof labeling scheme in constant-time if the vertices of a graph…
Recent work by Shehper et al. (2024) demonstrated that the well-known Akbulut-Kirby AK(3) balanced presentation of the trivial group is stably AC-equivalent to the trivial presentation. This result eliminates AK(3) as a potential…
The partial adiabatic search algorithm was introduced in [A. Tulsi, Phys. Rev. A 80, 052328 (2009)] as a modification of the usual adiabatic algorithm for quantum search with the idea that most of the interesting computation only happens…
Algorithms which compute properties over graphs have always been of interest in computer science, with some of the fundamental algorithms, such as Dijkstra's algorithm, dating back to the 50s. Since the 70s there as been interest in…
Ackermann's function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive…
The complexity class PPA consists of NP-search problems which are reducible to the parity principle in undirected graphs. It contains a wide variety of interesting problems from graph theory, combinatorics, algebra and number theory, but…
We provide a sound and relatively complete Hoare-like proof system for reasoning about partial correctness of recursive procedures in presence of local variables and the call-by-value parameter mechanism, and in which the correctness proofs…