Nondeterministic X-Machine

Download .pdf, .docx, .epub, .txt
Did you like this example?

CHAPTER 5

Formal Modeling

5.1 Overview

To achieve the maximum benefits from formal techniques, integration of approaches is required. In this chapter we present the integration of X-machine models and Z notation. The X-machine models sued to give the relationship between Z and X-machine are: (a) nondeterministic X-machine, (b) deterministic X-machine, (c) nondeterministic stream X-machine, (d) deterministic stream X-machine, (e) communicating stream X-machine, and (f) communicating stream X-machine system. The informal definitions of all these machines are taken from [1], [2], [3].

5.2 Design of Nondeterministic X-Machine

A Nondeterministic X-Machine is 10-tuple NXM = (X, Y, Z, α, β, Q, Φ, F, I, T) where:

1. X is a fundamental dataset on that the machine operates.

2. Y is a finite set of input alphabets.

3. Z is a finite set of output alphabets.

4. α and β are input and output partial functions, used to convert the input into the output sets from the fundamental sets, i. e., α: Y X and β: X Z.

5. Q is a finite nonempty set of states.

6. Φ is type of M, a set of relations on X, i. e., Φ: P (X  X). The notation (XX) denotes a set of all possible partial functions from X to X.

7. F is a next state partial function, a transition function, i. e., F: Q x φ  P Q, which takes a state a partial function and produces a new set of states.

8. I is a set of initial states, a subset of Q, and T is a set of terminal states, a subset of Q.

NXM
state:  Q
alphaIn:  SigmaIn
alphaOut:  SigmaOut
memory:  Memory
alpha:  (SigmaIn  Memory)
beta:  (SigmaOut  Memory)
function:  Memory  Memory
trans: Q  Memory  Memory   Q
I:  Q
T:  Q

state  
I  state
T  state
q, q1: Q; m, m1: Memory; i: SigmaIn; o: SigmaOut
 q  state  q1  state  m  memory  m1  memory  i  alphaIn

 o  alphaOut  m m1  function  i m  alpha  o m1  beta

 s, s1:  Q s  state  s1  state q m m1 s  trans

  q1 m m1 s1  trans q m m1 = q1 m m1  s = s1


Invariants:

a) The set of states states is a nonempty set.

b) The set of initial states I is a subset of states.

c) The set of final states T is a subset of states.

Do you want to see the Full Version?

View full version

Having doubts about how to write your paper correctly?

Our editors will help you fix any mistakes and get an A+!

Get started
Leave your email and we will send a sample to you.
Thank you!

We will send an essay sample to you in 24 Hours. If you need help faster you can always use our custom writing service.

Get help with my paper
Sorry, but copying text is forbidden on this website. You can leave an email and we will send it to you.