题目: 请设计DFA, 使其接受全部含有奇数个1的串, 假定 ∑ = {0, 1}.

解:

DFA可能出现两个个状态:

qeven: 读入了偶数个1的串.

qodd: 读入了奇数个1的串, 该状态也是终结状态(accept state).

它们的状态转移图如下:

编写程序, 运行效果如下:

测试用例说明:

0000不被上图的DFA接受

1111不被上图的DFA接受

1符合题目要求, 被DFA接受

0011001符合题目要求, 被DFA接受

空串不被DFA接受

0不被上图DFA接受

程序代码如下:

/* FSM-example2.c

* Using Deterministic Finite Automaton to recongnize

* a `0-1 string`

*

* Example2: Please design a DFA, accept every string

* containing odd numers of 1.

**/

#include

#include // calloc()

#include

enum {

STATE_even = 1, // Even number of 1 has readed

STATE_odd, // Odd number of 1 has readed

STATE_T // Accept state

};

typedef struct fsm_st {

int state;

int pos; // point to current pos

char buf[BUFSIZ];

}fsm_st;

fsm_st* myFsm;

void FSMdriver(fsm_st*);

void Hault(int);

int main() {

/* Create a FSM and initialize */

myFsm = (fsm_st*)calloc(0x1, sizeof(myFsm));

myFsm->state = STATE_even;

myFsm->pos = 0;

/* Read a string */

printf("Input a 01-string: ");

fgets(myFsm->buf, BUFSIZ, stdin);

/* Strat FSM */

while( myFsm->state != STATE_T ) {

FSMdriver(myFsm);

}

printf("Accept string!

");

free(myFsm);

return 0;

}

void FSMdriver(fsm_st* me) {

int pos = me->pos;

switch(me->state) {

case STATE_even:

if( me->buf[pos] == ‘1‘ ) {

me->state = STATE_odd;

me->pos++;

} else if( me->buf[pos] == ‘0‘ ) {

me->state = STATE_even;

me->pos++;

} else {

Hault(STATE_even);

}

break;

case STATE_odd:

if( me->buf[pos] == ‘0‘ ) {

me->state = STATE_T; // Terminated correctly

me->pos++;

} else if( me->buf[pos] == ‘1‘ ) {

me->state = STATE_even;

me->pos++;

} else {

me->state = STATE_T; // At the end stay in STATE_odd

}

break;

}

}

void Hault(int s) {

printf("FSM hault in STATE_%d

", s);

printf("FSM don‘t accept this string

");

free(myFsm);

exit(0);

}

DFA编程练习2