Creating Buchi Automaton to Accept Property

  • Thread starter dork
  • Start date
In summary, a buchi automaton is given that accepts the property of either p being true forever or p being true until q becomes true. It has three states, S0, S1, and S2, with S1 and S2 being the accepting states. From S0 to S1, the automaton loops if p is true and q is not true. From S1 to S2, it loops if either p is not true and q is true, or p is not true and q is not true. From S0 to S2, the automaton loops if both p and q are true. S1 also loops if p is true and q is not true, and S2 loops for any input. S
  • #1
dork
5
0

Homework Statement



Give a buchi automaton that accepts the following property
either p is true forever, or p is true until q becomes true

Homework Equations



check my answer if its right and correct if wrong


The Attempt at a Solution



Three states. Goes to p it loops and its final state.
or goes p then loops and if then goes q its final state and accepted
 
Physics news on Phys.org
  • #2
Three states.
S0, S1 AND S2.
S1 AND S2 ACCEPT STATES
FROM S0 TO S1 IF IT IS P AND NOT Q . FROM S1 TO S2 IF IT IS( P NOT Q) OR (NOT P AND Q)

FROM S0 TO S2 IF IT IS P AND Q .
ON S1 IT LOOPS IF IT IS P AND NOT Q.
S2 LOOPS FOR EVERYTHING
 
  • #3
S0 Is The Start State

Hope I Solved Everything Right.please Correct Me
 

1. What is a Buchi automaton?

A Buchi automaton is a type of finite state automaton that is used to determine whether an infinite input sequence satisfies a given property. It consists of a finite set of states, a set of input symbols, a transition function, and a set of accepting states.

2. How is a Buchi automaton created?

A Buchi automaton is typically created through a series of steps, including defining the alphabet of input symbols, constructing a transition table, determining the set of accepting states, and minimizing the automaton if necessary. These steps can vary slightly depending on the specific property that the automaton is being designed to accept.

3. What types of properties can a Buchi automaton accept?

Buchi automata are commonly used to accept properties related to infinite sequences, such as regular languages, LTL (Linear Temporal Logic) formulas, and ω-regular languages. They can also be used to verify properties of reactive systems, such as deadlock-freedom or liveness.

4. What are the advantages of using a Buchi automaton?

Buchi automata have several advantages, including being able to handle infinite inputs, being able to express complex properties, and being able to verify properties of reactive systems. They also have a simple and efficient construction process, making them a popular choice for formal verification tasks.

5. Are there any limitations to using a Buchi automaton?

Like any tool, Buchi automata also have limitations. They can only accept properties that are expressible in the automaton's formalism, and they may not always be the most efficient or intuitive choice for verifying certain types of systems. Additionally, they may not be suitable for handling large or complex properties due to the exponential growth of states and transitions as the property becomes more complex.

Similar threads

  • Set Theory, Logic, Probability, Statistics
2
Replies
54
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
20
Views
2K
  • Precalculus Mathematics Homework Help
Replies
2
Views
4K
  • Engineering and Comp Sci Homework Help
Replies
11
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
11
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
10
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
10
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
9
Views
2K
Back
Top