Related papers: Zero-Knowledge Proofs of the Conjugacy for Permuta…

We initiate the study of relativistic zero-knowledge quantum proof of knowledge systems with classical communication, formally defining a number of useful concepts and constructing appropriate knowledge extractors for all the existing…

Let $G$ be a closed highly homogeneous subgroup of $S_{\infty}$ not involving circular orderings. We show that the closure of a conjugacy class from $G$ contains a conjugacy class which is comeagre in it. Furthermore, we show that the…

We prove Union-Closed sets conjecture.

Often the question arises whether $Y$ can be predicted based on $X$ using a certain model. Especially for highly flexible models such as neural networks one may ask whether a seemingly good prediction is actually better than fitting pure…

NuLink provides privacy-preserving technology for decentralized applications via APIs. Users can securely store its valuable data, trade with others and so on. To ensure the privacy and security of service provided by NuLink,…

Let $p$ be a prime and let $\mathbb{C}$ be the complex field. We explicitly classify the finite solvable irreducible monomial subgroups of $\mathrm{GL}(p,\mathbb{C})$ up to conjugacy. That is, we give a complete and irredundant list of…

For a positively presented group G, we provide a criterion for two tuples of positive group generators of G to be Hurwitz equivalent or Hurwitz-conjugation equivalent. We also present an algorithmic approach to solve the Hurwitz equivalence…

A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuffle of words and languages. In this paper, we tackle the…

We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a…

It is shown that a natural notion of congruence permutability for quasivarieties already implies ``being a variety''. The result follows immediately from [3] and the sole aim of this note is to state it explicitly, together with a…

We construct a constant-round zero-knowledge classical argument for NP secure against quantum attacks. We assume the existence of Quantum Fully-Homomorphic Encryption and other standard primitives, known based on the Learning with Errors…

The conjugacy problem is one of the central questions in iteration theory. As far as we, for discontinuous strictly monotone maps there is no complete result. In this paper, we investigate the conjugacy problem of strictly monotone maps…

We characterise the group property of being with infinite conjugacy classes for wreath products of groups

We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…

Given a finite set of roots of unity, we show that all power sums are non-negative integers iff the set forms a group under multiplication. The main argument is purely combinatorial and states that for an arbitrary finite set system the…

A powerful feature in mechanism design is the ability to irrevocably commit to the rules of a mechanism. Commitment is achieved by public declaration, which enables players to verify incentive properties in advance and the outcome in…

In an earlier paper, we proved that Montgomery's Pair Correlation Conjecture (PCC) for zeros of the Riemann zeta-function can be used to prove without the assumption of the Riemann Hypothesis (RH) that asymptotically 100% of the zeros are…

We complete statement and proof for B. Moss\'e's unilateral recognizability theorem. We also provide an algorithm for deciding the unilateral non-recognizability of a given primitive substitution.

We consider zero knowledge interactive proofs in a richer, more realistic communication environment. In this setting, one may simultaneously engage in many interactive proofs, and these proofs may take place in an asynchronous fashion. It…

We prove the conjugacy of Sylow $p$-subgroups of linear pseudofinite groups under the assumption of the existence of a finite Sylow $p$-subgroup. We also give an example of a linear pseudofinite group with non-conjugate Sylow $2$-subgroups.