Related papers: On the structure of linear-time reducibility
Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved that if a constraint language has a weak near unanimity…
Ramsey quantifiers are a natural object of study not only for logic and computer science, but also for the formal semantics of natural language. Restricting attention to finite models leads to the natural question whether all Ramsey…
While prior work established a verifier-based polynomial-time framework for NP, explicit deterministic machines for concrete NP-complete problems have remained elusive. In this paper, we construct fully specified deterministic Turing…
There is a parallelism between Shannon information theory and algorithmic information theory. In particular, the same linear inequalities are true for Shannon entropies of tuples of random variables and Kolmogorov complexities of tuples of…
It is shown that in the multivariate case the orders p, of the AR part, and q, of the MA part, are not invariants of the time series. Thus, it is concluded that it only makes sense to define the class of ARMA(p,p)- irreducible models, where…
A regular realizability (RR) problem is testing nonemptiness of intersection of some fixed language (filter) with given regular language. We study here complexity of RR problems. It appears that for any language L there exists RR problem…
Any class of languages $\mathbf{L}$ accepted in time $\mathbf{T}$ has a counterpart $\mathbf{NL}$ accepted in nondeterministic time $\mathbf{NT}$. It follows from the definition of nondeterministic languages that $\mathbf{L} \subseteq…
The purpose of this letter is to investigate the time complexity consequences of the truncated Taylor series, known as Taylor Polynomials \cite{bakas2019taylor,Katsoprinakis2011,Nestoridis2011}. In particular, it is demonstrated that the…
Automatic differentiation (AD) aims to compute derivatives of user-defined functions, but in Turing-complete languages, this simple specification does not fully capture AD's behavior: AD sometimes disagrees with the true derivative of a…
Toda \cite{Toda} proved in 1989 that the (discrete) polynomial time hierarchy, $\mathbf{PH}$, is contained in the class $\mathbf{P}^{#\mathbf{P}}$, namely the class of languages that can be decided by a Turing machine in polynomial time…
Stephen Cook posited SAT is NP-Complete in 1971. If SAT is NP-Complete then, as is generally accepted, any polynomial solution of it must also present a polynomial solution of all NP decision problems. It is here argued, however, that NP is…
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…
Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In…
Results of computational complexity exist for a wide range of phrase structure-based grammar formalisms, while there is an apparent lack of such results for dependency-based formalisms. We here adapt a result on the complexity of…
Given a neural network, training data, and a threshold, it was known that it is NP-hard to find weights for the neural network such that the total error is below the threshold. We determine the algorithmic complexity of this fundamental…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
This paper considers the question of P = NP in context of the polynomial time SAT algorithm. It posits proposition dependent on existence of conjectured problem that even where the algorithm is shown to solve SAT in polynomial time it…
The Curry-Howard correspondence is often called the proofs-as-programs result. I offer a generalization of this result, something which may be called machines as programs. Utilizing this insight, I introduce two new Turing Machines called…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
We show the equivalence between a probabilistic Turing machine and the time evolution of a one-dimensional Ising model, the Glauber model in one dimension, equilibrium positions representing the results of computations of the Turing…