Discreteness is undecidable

Discreteness is undecidable

Question 1.1. Let G be a connected Lie group and let A = (A1, . . . , Ak) be a finite ordered subset of G. Is the discreteness problem for the subgroup ΓA := 〈A1, . . . , Ak〉 < G decidable? This question, in the case of G = PSL(2,C), was raised, most recently, in the paper [8] by J. Gilman and L. Keen, who noted that “it is a challenging problem that has been investigated for more than a centur...

System NEL is Undecidable

System NEL is a conservative extension of multiplicative exponential linear logic (extended by the rules mix and nullary mix) by a self-dual noncommutative connective called seq which has an intermediate position between the connectives par and times. In this paper, I will show that system NEL is undecidable by encoding two counter machines into NEL. Although the encoding is simple, the proof o...

Rigidity is undecidable

We show that the problem ‘whether a finite set of regular-linear axioms defines a rigid theory’ is undecidable. 2010 Mathematical Subject Classification 03D35, 03C05, 03G30, 18C10, 18C15

Quasi-Linearizability is Undecidable

Quasi-linearizability is a quantitative relaxation of linearizability. It preserves the intuition of the standard notion of linearizability and permits more flexibility. The decidability of quasi-linearizability has been remaining open in general for a bounded number of processes. In this paper we show that the problem of whether a library is quasilinearizable with respect to a regular sequenti...

Whitehead's Problem is Undecidable