We call a run *bounded* by $b\in\N$ if $c_i\le b$ for all $0\le i\le k$.

For any fixed initial configuration $(s,c)$, we define its *language* $\Lang[\?A]{s,c}\subseteq\alphabet^*$ to contain exactly all words on which an accepting run starting in $(s,c)$ exists. (We omit the subscript $\?A$ if the OCN is clear from context.) Similarly, the *$b$-bounded language* $\bLang{s,c}{b}$ is the set of those words on which there is a $b$-bounded run starting in $(s,c)$.

The OCN is *deterministic* if for every pair $(s,a) \in Q\x\alphabet$ there is at most one pair $(d,q)\in\N\x Q$ with $(s,a,d,s')\in\delta$. A net together with an initial configuration $(\initialstate,c_0)$ is *unambiguous* if for every word $w\in\alphabet^*$ there is at most one accepting run starting in $(\initialstate,c_0)$.

##### Two-Counter Machines. {#two-counter-machines. .unnumbered}

A two-counter machine (Minsky Machine) $\M$ is a sequence $(l_1,\ldots,l_n)$ of commands involving two counters $x$ and $y$. We refer to $\set{1,\ldots,n}$ as the [*locations*]{} of the machine. There are five possible forms of commands: `inc(c)`, `dec(c)`, `goto l_i`, `halt`, `if c=0 goto l_i else goto l_j`, where $c\in \set{x,y}$ is a counter and $1\le i,j\le n$ are locations. The counters are initially set to $0$. Since we can always check whether $c=0$ before a $\texttt{dec(c)}$ 