Tautology (structure)

tautology

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 10061		Accepted: 3826

Description

WFF ' N PROOF is a logic game played with dice. Each die has six faces representing some subset of the possible symbols K, A, N, C, E, p, Q, R, S, T. A well-formed formula (WFF) is any string of these symbols obeying the following rules:

• P, Q, R, S, and T are wffs
• If w is a WFF, N-w is a WFF
• If w and x are wffs, Kwx, Awx, Cwx, and Ewx is wffs.

The meaning of a WFF is defined as follows:

• P, Q, R, S, and T is logical variables that could take on the value 0 (false) or 1 (true).
• K, A, N, C, E mean and , or, not, implies, and equals as defined in the truth table below .

Definitions of K, A, N, C, and E

  w    x	K wx	A WX	N w	C wx	E wx
1  1	1	1	0	1	1
1  0	0	1	0	0	0
0  1	0	1	1	1	0
0 0	0	0	1	1	1

A tautology is a WFF that have value 1 (true) regardless of the values of its variables. For example, Apnp are a tautology because it is true regardless of the value of p. On the other hand, apnq was not , because it had the value 0 for p=0, Q=1.

You must determine whether or not a WFF is a tautology.

Input

Input consists of several test cases. Each test case was a single line containing a WFF with no more than symbols. A line containing 0 follows.

Output

For each test case, the output a line containing tautology or not as appropriate.

Sample Input

ApNpApNq0

Sample Output

Tautologynot

Source

Waterloo Local Contest, 2006.9.30

1#include <stdio.h>2#include <string.h>3#include <iostream>4 using namespacestd;5 intp, Q, R, S, T;6 intk[2][2] = {0,0,0,1}, a[2][2] = {0,1,1,1}, n[2] = {1,0}, c[2][2] = {1,1,0,1}, e[2][2] = {1,0,0,1} ;7 stringSt;8 intNow ;9 BOOLFlag;Ten  One intCalc () A { -now++ ; -     Switch(St[now]) the     { -          Case 'K':returnK[calc ()][calc ()]; -          Case 'A':returnA[calc ()][calc ()]; -          Case 'N':returnN[calc ()]; +          Case 'C':returnC[calc ()][calc ()]; -          Case 'E':returnE[calc ()][calc ()]; +          Case 'P':returnp; A          Case 'Q':returnQ; at          Case 'R':returnR; -          Case 's':returns; -          Case 'T':returnT; -     } - } - intMain () in { -    //freopen ("A.txt", "R", stdin); to      while(Cin >> St && St! ="0") { +Flag =0 ; -          for(P =0; P <2&&!flag; p++) the              for(q =0; Q <2&&!flag; q++) *                  for(R =0; R <2&&!flag; r++) $                      for(s =0; s <2&&!flag; s++)Panax Notoginseng                          for(t =0; T <2&&!flag; t++) { -now =-1 ; the                             if( !Calc ()) +Flag =true ; A                         } the         if(flag) +Puts (" not") ; -         Else $Puts ("tautology") ; $     } -     return 0 ; -}

View Code

Pretty use of backtracking.
Reprint: http://blog.csdn.net/allenlsy/article/details/4885948

Tautology: The Chinese is called the condom theory, or the eternal Truth, that is, no matter how the variable change in the bitwise operation, the final answer is 1

The implies in the title refers to the implication, when and only if (condition q = 1) ----> (conclusion s = 0) is false and the rest is true

Tautology (structure)