= Modular machine
{title2=$\mathcal M$}
A modular machine of modulus $m>1$ acts on pairs in $\mathbb N^2$. Each instruction $(a,b,c,R)$ or $(a,b,c,L)$ has $0\le a,b<m$ and $0\le c<m^2$, and at most one instruction is assigned to each residue pair $(a,b)$. The two transition types are $(mu+a,mv+b)\mapsto(m^2u+c,v)$ and $(mu+a,mv+b)\mapsto(u,m^2v+c)$. These finite arithmetic operations can encode a <Turing machine>; a designated terminal configuration can have a nonrecursive <halting set>.
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