$$v\in N V a r$$
$$\oplus$$
$$e_{1}\,\oplus\,e_{2}$$. 
The special symbols true false, parentheses and comma.

The set of arithmetic expressions is constructed from the following rules:

1. Every numerical state variable v 2 NVar is an arithmetic expression.

2. A natural number is an arithmetic expression.

$$F o r m$$
is an arithmetic expression.

$$v\in P\,V a r$$
$$e_{\,2}$$
$$e\,_{1}\quad\quad e\,_{2}$$. 
a formula.

Parentheses have their usual meaning and operators have their usual priority and associativity with the if-then-else operator \ " given lowest priority.

$$e_{1}\qquad\quad e_{2}$$
3. If e1 and e2 are arithmetic expressions and  is an arithmetic operator, then e1  e2

Finally, the set of formulas Form is generated by the rules:

$$t r u e$$
$$f a l s e$$
1. true and false are formulas.

2. Propositional state variables v 2 PVar are formulas.

$$e_{1}$$
3. If e1 and e2 are arithmetic expressions and is a relation operator, then e1 e2 is
4. If f1 f2 and f3 are formulas, so are ( f1), (f1 f2), (f1 f2), (f1 f2), (f1 , f2 and (f1 f2; f3).

$f_{1}$$f_{2},f_{3}$$v\in NVar$$rng$$v$$f_{1}$$f_{2}$$f_{1}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$$f_{1}$$f_{2}$$f_{3}$$v$\(f_{1

$$\mathrm{N}\qquad M$$
terms of an NFA M

  \begin{tabular}{l l l l l}  & $B$ & $M$ & $True,\,False$ & $characteristics$ \\ _function_ $A$ & $B$ & $A\subseteq B$ & $A$ & $x\in A$ \\ N & $M$ & $\begin{array}{l}\mbox{\it transition relation}T\subseteq Q\times&\times Q\\ \mbox{\it$s,i,s^{\prime}$}\end{array}$ & $s^{\prime}\in\delta$ & $s,i$ & \\  & $Q$ & $M$ & & $Q$ & $PVar$ \\ $B$ & $\times$ _Near_ & N & & & $M$ \\ \end{tabular}  

SForm  Form is subset of the formulas only referring to current state variables.

These formulas are called state formulas 4.2 Semantics Denition 1 (NFA) A Non-deterministic Finite Automaton is a 3-tuple, M = (Q; ;  , where Q is a set of states, is a set of input values, and  Q - Qis a next state function.

3. Note: the characteristic function has the same name as the set.

