解析 – 如何解决三元表达式(a？b：c)和“可能”表达式(a？)之间的LR(1)语法歧义？

(0) exp1: ternary;
(1) exp1: exp2;
(2) ternary: exp2 "?" exp1 ":" exp1;
(3) exp2: exp2 "+" exp3;
(4) exp2: exp3;
(5) exp3: maybe;
(6) exp3: "1";
(7) maybe: exp3 "?";

我相信这种语言是明确的,应该是LR可解析的. (如果我错了,请告诉我！)

但是,当我尝试为这个语法生成一个LR(1)解析器时,我得到了shift / reduce冲突,因为当解析器看到带有lookahead的exp3时,它不知道是要移位还是减少：

Conflicts in state 3:
    Reduction using rule 4: exp2:  exp3 · | "?"
    Shift to state 6

Conflicts in state 9:
    Reduction using rule 3: exp2:  exp2 "+" exp3 · | "?"
    Shift to state 6

Conflicts in state 13:
    Reduction using rule 4: exp2:  exp3 · | "?"
    Shift to state 16

Conflicts in state 20:
    Reduction using rule 4: exp2:  exp3 · | "?"
    Shift to state 23

Conflicts in state 25:
    Reduction using rule 3: exp2:  exp2 "+" exp3 · | "?"
    Shift to state 23

Conflicts in state 28:
    Reduction using rule 3: exp2:  exp2 "+" exp3 · | "?"
    Shift to state 16

有没有合理的方法让我使这种语言LR(1) – 可分解(没有冲突)？

或者GLR(或LR(2)？)是我这样的语言的唯一现实选择？
(或者我甚至错误地认为语言首先是明确的？)

作为参考,我生成的模糊状态机如下(其中♦是EOF)：

State 0:
    exp1:  · ternary | {♦} → shift 1
    ternary:  · exp2 "?" exp1 ":" exp1 | {♦} → shift 2
    exp2:  · exp2 "+" exp3 | {"?","+"} → shift 2
    exp2:  · exp3 | {"?","+"} → shift 3
    exp3:  · maybe | {"?","+"} → shift 4
    exp3:  · "1" | {"?","+"} → shift 5
    maybe:  · exp3 "?" | {"?","+"} → shift 3

State 1:
    exp1:  ternary · | {♦} → reduce 0

State 2:
    ternary:  exp2 · "?" exp1 ":" exp1 | {♦} → shift 7
    exp2:  exp2 · "+" exp3 | {"?","+"} → shift 8

State 3:
    exp2:  exp3 · | {"+"} → reduce 4
    exp2:  exp3 · | {"?"} → reduce 4 shift 6
    maybe:  exp3 · "?" | {"?","+"} → reduce 4 shift 6

State 4:
    exp3:  maybe · | {"?","+"} → reduce 5

State 5:
    exp3:  "1" · | {"?","+"} → reduce 6

State 6:
    maybe:  exp3 "?" · | {"?","+"} → reduce 7

State 7:
    exp1:  · ternary | {":"} → shift 10
    exp1:  · exp2 | {":"} → shift 11
    ternary:  · exp2 "?" exp1 ":" exp1 | {":"} → shift 11
    ternary:  exp2 "?" · exp1 ":" exp1 | {♦} → shift 12
    exp2:  · exp2 "+" exp3 | {"?",":","+"} → shift 11
    exp2:  · exp3 | {"?","+"} → shift 13
    exp3:  · maybe | {"?","+"} → shift 14
    exp3:  · "1" | {"?","+"} → shift 15
    maybe:  · exp3 "?" | {"?","+"} → shift 13

State 8:
    exp2:  exp2 "+" · exp3 | {"?","+"} → shift 9
    exp3:  · maybe | {"?","+"} → shift 9

State 9:
    exp2:  exp2 "+" exp3 · | {"+"} → reduce 3
    exp2:  exp2 "+" exp3 · | {"?"} → reduce 3 shift 6
    maybe:  exp3 · "?" | {"?","+"} → reduce 3 shift 6

State 10:
    exp1:  ternary · | {":"} → reduce 0

State 11:
    exp1:  exp2 · | {":"} → reduce 1
    ternary:  exp2 · "?" exp1 ":" exp1 | {":"} → shift 26
    exp2:  exp2 · "+" exp3 | {"?","+"} → shift 27

State 12:
    ternary:  exp2 "?" exp1 · ":" exp1 | {♦} → shift 17

State 13:
    exp2:  exp3 · | {":","+"} → reduce 4
    exp2:  exp3 · | {"?"} → reduce 4 shift 16
    maybe:  exp3 · "?" | {"?","+"} → reduce 4 shift 16

State 14:
    exp3:  maybe · | {"?","+"} → reduce 5

State 15:
    exp3:  "1" · | {"?","+"} → reduce 6

State 16:
    maybe:  exp3 "?" · | {"?","+"} → reduce 7

State 17:
    exp1:  · ternary | {♦} → shift 1
    exp1:  · exp2 | {♦} → shift 18
    ternary:  · exp2 "?" exp1 ":" exp1 | {♦} → shift 18
    ternary:  exp2 "?" exp1 ":" · exp1 | {♦} → shift 19
    exp2:  · exp2 "+" exp3 | {♦,"?","+"} → shift 18
    exp2:  · exp3 | {♦,"+"} → shift 20
    exp3:  · maybe | {♦,"+"} → shift 21
    exp3:  · "1" | {♦,"+"} → shift 22
    maybe:  · exp3 "?" | {♦,"+"} → shift 20

State 18:
    exp1:  exp2 · | {♦} → reduce 1
    ternary:  exp2 · "?" exp1 ":" exp1 | {♦} → shift 7
    exp2:  exp2 · "+" exp3 | {♦,"+"} → shift 24

State 19:
    ternary:  exp2 "?" exp1 ":" exp1 · | {♦} → reduce 2

State 20:
    exp2:  exp3 · | {♦,"+"} → reduce 4
    exp2:  exp3 · | {"?"} → reduce 4 shift 23
    maybe:  exp3 · "?" | {♦,"+"} → reduce 4 shift 23

State 21:
    exp3:  maybe · | {♦,"+"} → reduce 5

State 22:
    exp3:  "1" · | {♦,"+"} → reduce 6

State 23:
    maybe:  exp3 "?" · | {♦,"+"} → reduce 7

State 24:
    exp2:  exp2 "+" · exp3 | {♦,"+"} → shift 25
    exp3:  · maybe | {♦,"+"} → shift 25

State 25:
    exp2:  exp2 "+" exp3 · | {♦,"+"} → reduce 3
    exp2:  exp2 "+" exp3 · | {"?"} → reduce 3 shift 23
    maybe:  exp3 · "?" | {♦,"+"} → reduce 3 shift 23

State 26:
    exp1:  · ternary | {":"} → shift 10
    exp1:  · exp2 | {":"} → shift 11
    ternary:  · exp2 "?" exp1 ":" exp1 | {":"} → shift 11
    ternary:  exp2 "?" · exp1 ":" exp1 | {":"} → shift 29
    exp2:  · exp2 "+" exp3 | {"?","+"} → shift 13

State 27:
    exp2:  exp2 "+" · exp3 | {"?","+"} → shift 28
    exp3:  · maybe | {"?","+"} → shift 28

State 28:
    exp2:  exp2 "+" exp3 · | {":","+"} → reduce 3
    exp2:  exp2 "+" exp3 · | {"?"} → reduce 3 shift 16
    maybe:  exp3 · "?" | {"?","+"} → reduce 3 shift 16

State 29:
    ternary:  exp2 "?" exp1 · ":" exp1 | {":"} → shift 30

State 30:
    exp1:  · ternary | {":"} → shift 10
    exp1:  · exp2 | {":"} → shift 11
    ternary:  · exp2 "?" exp1 ":" exp1 | {":"} → shift 11
    ternary:  exp2 "?" exp1 ":" · exp1 | {":"} → shift 31
    exp2:  · exp2 "+" exp3 | {"?","+"} → shift 13

State 31:
    ternary:  exp2 "?" exp1 ":" exp1 · | {":"} → reduce 2