Verifying identical communicating processes is undecidable

Verifying Identical Communicating Processes is Undecidable

We prove that boundedness and reachability tree niteness are undecidable for systems of two identical automata communicating via two perfect unbounded oneway FIFO channels and constructed solely from cycles about their initial states. Using a form of mutual exclusion for such systems, we prove further that undecidability holds even when the identical automata are totally indistinguishable in th...

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