The ancient calculator logic in total

The ancient calculator logic (けいさんきろんり, Computational Tree Logic, CTL) in total is a kind of the divergence talking with each other law of nature. I diverge like hierarchy structure without being decided in the model in the future in that time. One of future plural courses really becomes the real course.

Table of contents

Grammar

${\displaystyle \phi ::=F|T|p|(\neg \phi) |(\phi \land \phi) |(\phi \lor \phi) |(\phi \rightarrow \phi) |AX\phi |EX\phi |AF\phi |EF\phi |AG\phi |EG\phi |A[\phi U\phi ]|E[\phi U\phi]}$ 

Here, p is item atom. A expresses "along All Paths (necessarily) about all courses", and "at least one course exists, and E expresses along at least there Exists one path" (sometimes). For example, it is 整論理式 of CTL as follows.

${\displaystyle EFEGp\rightarrow AFr}$ 

However, it is not 整論理式 of CTL as follows.

${\displaystyle EF(rUq)}$ 

The problems of this character string are the points that do not protect a sentence structure rule that it is A by all means that is done a preliminary remark by U or must be E.

CTL uses vocabulary of the first-order predicate logic as a component and generates the Boolean expression that brought the aspect operator of the aspect into it more at time.

Operator

Logic operator

The logic operator ${\displaystyle \neg ,\lor ,\land ,\rightarrow}$  や ${\displaystyle \leftrightarrow}$  It is like the といった public. In addition, I may use fixed number true and false of the Boolean.

Time aspect operator

To a time aspect operator with the following:

• Course operator (Path Operators)
  • A ${\displaystyle \phi}$  - All: ${\displaystyle \phi}$  It is the truth by all courses diverging from a state as of は.
  • E ${\displaystyle \phi}$  - Exists: It is at least one course now in courses diverging from a state ${\displaystyle \phi}$  But, it is the truth.
• State operator (State Operators)
  • N ${\displaystyle \phi}$  - Next: ${\displaystyle \phi}$  It is the truth in the state of the は next (I may be transcribed into X).
  • G ${\displaystyle \phi}$  - Globally: ${\displaystyle \phi}$  It is always the truth by all courses after はその.
  • F ${\displaystyle \phi}$  - Finally: ${\displaystyle \phi}$  It becomes the truth at the time of either of the course after はその.
  • ${\displaystyle \phi}$  U ${\displaystyle \psi}$  - Until: ${\displaystyle \phi}$  Oh, it is a certain point in time ${\displaystyle \psi}$  But, it is the truth until it becomes the truth. This is the future ${\displaystyle \psi}$  But, I mean that it is inspected whether it is the truth.
  • ${\displaystyle \phi}$  W ${\displaystyle \psi}$  - Weak until: ${\displaystyle \phi}$  Oh,${\displaystyle \psi}$  But, it is the truth until it becomes the truth. The difference with U is the future ${\displaystyle \psi}$  But, that it is the truth is a point without an inspected guarantee. I call it the "unless"" operator.

In CTL*, I can mix the aspect operator freely at time. The operators are grouped to two as above in CTL, and only the combination of course operator and in condition operators is possible. See a later example.

The smallest set of the operator

There is the smallest set of the operator in CTL. I can transfer the Boolean expression of all CTL to the Boolean expression only as for this smallest set. In the case of model checking, this is convenient. As an example of the smallest set {false, ${\displaystyle \lor ,\neg}$ There are, EG, EU, EX}.

Below indicating the example of the renewal about the time aspect operator:

• EF${\displaystyle \phi}$  == E[trueU${\displaystyle \phi}$ ]
• AX${\displaystyle \phi}$  == ${\displaystyle \neg}$ EX${\displaystyle \neg}$ ${\displaystyle \phi}$ )
• AG${\displaystyle \phi}$  == ${\displaystyle \neg}$ EF${\displaystyle \neg}$ ${\displaystyle \phi}$  == ${\displaystyle \neg}$  E[trueU${\displaystyle \neg}$ ${\displaystyle \phi}$ ]
• AF${\displaystyle \phi}$  == A[1U${\displaystyle \phi}$ ] = = ${\displaystyle \neg}$ EG${\displaystyle \neg}$ ${\displaystyle \phi}$ )
• A[${\displaystyle \phi}$ U${\displaystyle \psi}$ ] = = ${\displaystyle \neg}$ (E[${\displaystyle \neg}$ ${\displaystyle \psi}$ U${\displaystyle \neg}$ (${\displaystyle \phi}$  ${\displaystyle \lor}$  ${\displaystyle \psi}$ ] ${\displaystyle \lor}$  EG ${\displaystyle \neg}$  ${\displaystyle \psi}$ )

Example

A meaning of P says, "I like chocolate", and a meaning of Q says, "the outside is warm".

AG.P

Even if there will be what in future, I like chocolate.

EF.P

The day when I come to like chocolate soon sometime soon may come.

AF.EG.P

One day (AF), I absolutely come to like chocolate and remain in a favorite state forever. (I am careful about few points in the life enthusiasts, and the human life is limited, but G expresses infinity)

EG.AF.P

It is the crossroads that is serious in my life now. By getting up next; I am (AF) coming to like chocolate by all means sometime all the time (G) (E), the future. However, the situations are totally different, and I cannot guarantee it when a bad thing happens next whether it is to a chocolate enthusiast.

A(PUQ)

I will like chocolate every day in future until the outside becomes warm. However, the guarantee that I already like chocolate disappears once if the outside becomes warm. In addition, the outside is guaranteed in the future for one day when time becoming warm comes.

E((EX.P)U(AG.Q))

(E) where has the following possibilities. (AG.Q) where the outside becomes warm all the time from one day. (EX.P) where there are always some kind of opportunities when I come to like chocolate on the next day until the day.

with other logic of relationships

Ancient calculator logic (CTL) in total is a subset of CTL* like linear time talking with each other law of nature (LTL). CTL and LTL have the common part, too, but are not equivalent.

• There is GF.P in LTL, but CTL does not have it.
• AG(P${\displaystyle \rightarrow}$ (EF.Q)) It is in は CTL, but LTL does not have it.

Allied item

• Linear time talking with each other law of nature

References

• Michael Huth and Mark Ryan (2004). Logic in Computer Science(Second Edition). Cambridge University Press. pp. 207. ISBN 0-521-54310-X. 
• Emerson, E. A. and Halpern, J. Y. (1985). "Decision procedures and expressiveness in the temporal logic of branching time." Journal of Computer and System Sciences 30 (1): 1-24. 
• Clarke, E. M., Emerson, E. A., and Sistla, A. P. (1986). "Automatic verification of finite-state concurrent systems using temporal logic specifications." ACM Transactions on Programming Languages and Systems 8 (2): 244-263. 
• Emerson, E. A. (1990). "Temporal and modal logic." In J. van Leeuwen (ed.). Handbook of Theoretical Computer Science, vol. B. MIT Press. pp. pp. 955-1072. ISBN 0-262-22039-3. 

It is acquired by "https://ja.wikipedia.org/w/index.php?title= calculation tree logic &oldid=60398089"

This article is taken from the Japanese Wikipedia The ancient calculator logic in total

This article is distributed by cc-by-sa or GFDL license in accordance with the provisions of Wikipedia.

Wikipedia and Tranpedia does not guarantee the accuracy of this document. See our disclaimer for more information.

In addition, Tranpedia is simply not responsible for any show is only by translating the writings of foreign licenses that are compatible with CC-BY-SA license information.