Related papers: Constructive membership testing in black-box class…
We introduce a new constructive recognition algorithm for finite special linear groups in their natural representation. Given a group $G$ generated by a set of $d\times d$ matrices over a finite field $\mathbb{F}_q$, known to be isomorphic…
We construct a finitely presented group with coNP-complete word problem, and a finitely generated simple group with coNP-complete word problem. These groups are represented as Thompson groups, hence as partial transformation groups of…
We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
We consider the following problem: Given a set S of at most n elements from a universe of size m, represent it in memory as a bit string so that membership queries of the form "Is x in S?" can be answered by making at most t probes into the…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
In recent years we have explored using Haskell alongside a traditional mathematical formalism in our large-enrolment university course on topics including logic and formal languages, aiming to offer our students a programming perspective on…
We present Las Vegas algorithms for constructive recognition and constructive membership testing of the Ree groups 2G_2(q) = Ree(q), where q = 3^{2m + 1} for some m > 0, in their natural representations of degree 7. The input is a…
The conjugacy problem for a finitely generated group $G$ is the two-variable problem of deciding for an arbitrary pair $(u,v)$ of elements of $G$, whether or not $u$ is conjugate to $v$ in $G$. We construct examples of finitely generated,…
The global testing problem studied in this paper is to seek a definite answer to whether a system of concurrent black-boxes has an observable behavior in a given finite (but could be huge) set "Bad". We introduce a novel approach to solve…
An important endeavor in computer science is to understand the expressive power of logical formalisms over discrete structures, such as words. Naturally, "understanding" is not a mathematical notion. This investigation requires therefore a…
We investigate the computational complexity of various decision problems related to conjugacy in finite inverse semigroups. We describe polynomial-time algorithms for checking if two elements in such a semigroup are ~p conjugate and whether…
We examine the computational complexity of problems in which we are given generators for a partial bijection semigroup and asked to check properties of the generated semigroup. We prove that the following problems are in AC$^0$: (1)…
Let $\Omega$ be a finite set of finitary operation symbols. An $\Omega$-expanded group is a group (written additively and called the additive group of the $\Omega$-expanded group) with an $\Omega$-algebra structure. We use the black-box…
The assembly index of assembly theory quantifies the minimal number of composition steps required to construct an object from elementary components. The study proves that the decision version of the assembly index problem is NP-complete,…
Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this…
Lists of equivalence classes of words under rotation or rotation plus reversal (i.e., necklaces and bracelets) have many uses, and efficient algorithms for generating these lists exist. In combinatorial group theory elements of a group are…
We estimate the proportion of several classes of elements in finite classical groups which are readily recognised algorithmically, and for which some power has a large fixed point subspace and acts irreducibly on a complement of it. The…
In this paper we consider the problem of testing whether two finite groups are isomorphic. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of…