Start of CONSTRUCTOR for the Grammar G9.grm Sat Apr 03 15:57:14 2004
Terminal alphabet
# 1 = #
# 2 = a
# 3 = b
# 4 = 1
# 5 = c
# 6 = d
Nonterminal alphabet
# 7 = `T'
# 8 = `S'
# 9 = `A'
#10 = `B'
Productions
P 1: `T' -> # `S' #
P 2: `S' -> a `A' a
P 3: `S' -> b `A' b
P 4: `S' -> a `B' b
P 5: `S' -> b `B' a
P 6: `A' -> 1
P 7: `B' -> 1
P 8: `A' -> `A' c
P 9: `B' -> d `B'
Leftmost-set
Symbol | # | a | b | 1 | c | d | T | S | A | B |
7.T | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8.S | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
9.A | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | * | 0 |
10.B | 0 | 0 | 0 | * | 0 | * | 0 | 0 | 0 | 0 |
Rightmost-set
Symbol | # | a | b | 1 | c | d | T | S | A | B |
7.T | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8.S | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
9.A | 0 | 0 | 0 | * | * | 0 | 0 | 0 | 0 | 0 |
10.B | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | * |
Leftmost & rightmost sets
`T' leftmost set: `#'
`T' rightmost set: #
`S' leftmost set: `a' , `b'
`S' rightmost set: a , b
`A' leftmost set: `1' , `A'
`A' rightmost set: 1 , c
`B' leftmost set: `1' , `d'
`B' rightmost set: 1 , B
Precedence matrix
Symbol | # | a | b | 1 | c | d | T | S | A | B |
1.# | 0 | < | < | 0 | 0 | 0 | 0 | = | 0 | 0 |
2.a | > | 0 | 0 | < | 0 | < | 0 | 0 | 3 | = |
3.b | > | 0 | 0 | < | 0 | < | 0 | 0 | 3 | = |
4.1 | 0 | > | > | 0 | > | 0 | 0 | 0 | 0 | 0 |
5.c | 0 | > | > | 0 | > | 0 | 0 | 0 | 0 | 0 |
6.d | 0 | 0 | 0 | < | 0 | < | 0 | 0 | 0 | = |
7.T | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8.S | = | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
9.A | 0 | = | = | 0 | = | 0 | 0 | 0 | 0 | 0 |
10.B | 0 | 5 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
The relationships of symbol #1 #:
The relationships of symbol #2 a:
> # | < 1 | < d | <= `A' | = `B' |
The relationships of symbol #3 b:
> # | < 1 | < d | <= `A' | = `B' |
The relationships of symbol #4 1:
The relationships of symbol #5 c:
The relationships of symbol #6 d:
The relationships of symbol #7 `T':
The relationships of symbol #8 `S':
The relationships of symbol #9 `A':
The relationships of symbol #10 `B':
Precedence varies
P2-conflict: a <= `A'
The source is the production P 2: `S' -> a `A' a
I'll add a new NT P10: `S1' -> `A' a
I'll change the production P 2: `S' -> a `S1'
P2-conflict: b <= `A'
The source is the production P 3: `S' -> b `A' b
I'll add a new NT P11: `S2' -> `A' b
I'll change the production P 3: `S' -> b `S2'
Leftmost-set
Symbol | # | a | b | 1 | c | d | T | S | A | B | S1 | S2 |
7.T | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8.S | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
9.A | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | * | 0 | 0 | 0 |
10.B | 0 | 0 | 0 | * | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 |
11.S1 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | * | 0 | 0 | 0 |
12.S2 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | * | 0 | 0 | 0 |
P1-conflict: `B' => a
The source is the production P 5: `S' -> b `B' a
I'll add a new NT P12: `S3' -> b `B'
I'll change the production P 5: `S' -> `S3' a
P1-conflict: `B' => b
The source is the production P 4: `S' -> a `B' b
I'll add a new NT P13: `S4' -> a `B'
I'll change the production P 4: `S' -> `S4' b
New grammar
P 1: `T' -> # `S' #
P 2: `S' -> a `S1'
P 3: `S' -> b `S2'
P 4: `S' -> `S4' b
P 5: `S' -> `S3' a
P 6: `A' -> 1
P 7: `B' -> 1
P 8: `A' -> `A' c
P 9: `B' -> d `B'
P10: `S1' -> `A' a
P11: `S2' -> `A' b
P12: `S3' -> b `B'
P13: `S4' -> a `B'
Leftmost-set
Symbol | # | a | b | 1 | c | d | T | S | A | B | S1 | S2 | S3 | S4 |
7.T | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8.S | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | * | * |
9.A | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 |
10.B | 0 | 0 | 0 | * | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
11.S1 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 |
12.S2 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 |
13.S3 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
14.S4 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Rightmost-set
Symbol | # | a | b | 1 | c | d | T | S | A | B | S1 | S2 | S3 | S4 |
7.T | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8.S | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | * | * | 0 | 0 |
9.A | 0 | 0 | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
10.B | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 |
11.S1 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
12.S2 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
13.S3 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 |
14.S4 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 |
Leftmost & rightmost sets
`T' leftmost set: `#'
`T' rightmost set: #
`S' leftmost set: `a' , `b' , `S3' , `S4'
`S' rightmost set: a , b , S1 , S2
`A' leftmost set: `1' , `A'
`A' rightmost set: 1 , c
`B' leftmost set: `1' , `d'
`B' rightmost set: 1 , B
`S1' leftmost set: `1' , `A'
`S1' rightmost set: a
`S2' leftmost set: `1' , `A'
`S2' rightmost set: b
`S3' leftmost set: `b'
`S3' rightmost set: 1 , B
`S4' leftmost set: `a'
`S4' rightmost set: 1 , B
Precedence matrix
Symbol | # | a | b | 1 | c | d | T | S | A | B | S1 | S2 | S3 | S4 |
1.# | 0 | < | < | 0 | 0 | 0 | 0 | = | 0 | 0 | 0 | 0 | < | < |
2.a | > | 0 | 0 | < | 0 | < | 0 | 0 | < | = | = | 0 | 0 | 0 |
3.b | > | 0 | 0 | < | 0 | < | 0 | 0 | < | = | 0 | = | 0 | 0 |
4.1 | 0 | > | > | 0 | > | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
5.c | 0 | > | > | 0 | > | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
6.d | 0 | 0 | 0 | < | 0 | < | 0 | 0 | 0 | = | 0 | 0 | 0 | 0 |
7.T | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8.S | = | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
9.A | 0 | = | = | 0 | = | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
10.B | 0 | > | > | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
11.S1 | > | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
12.S2 | > | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
13.S3 | 0 | = | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
14.S4 | 0 | 0 | = | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
The relationships of symbol #1 #:
< a | < b | = `S' | < `S3' | < `S4' |
The relationships of symbol #2 a:
> # | < 1 | < d | < `A' | = `B' | = `S1' |
The relationships of symbol #3 b:
> # | < 1 | < d | < `A' | = `B' | = `S2' |
The relationships of symbol #4 1:
The relationships of symbol #5 c:
The relationships of symbol #6 d:
The relationships of symbol #7 `T':
The relationships of symbol #8 `S':
The relationships of symbol #9 `A':
The relationships of symbol #10 `B':
The relationships of symbol #11 `S1':
The relationships of symbol #12 `S2':
The relationships of symbol #13 `S3':
The relationships of symbol #14 `S4':
Grammar G9.grm is a precedence grammar
Grammar G9.grm is not invertible
Left Context
Symbol | # | a | b | 1 | c | d | T | S | A | B | S1 | S2 | S3 | S4 |
7.T | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8.S | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
9.A | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
10.B | 0 | * | * | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
11.S1 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
12.S2 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
13.S3 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
14.S4 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Right Context
Symbol | # | a | b | 1 | c | d |
7.T | 0 | 0 | 0 | 0 | 0 | 0 |
8.S | * | 0 | 0 | 0 | 0 | 0 |
9.A | 0 | * | * | 0 | * | 0 |
10.B | 0 | * | * | 0 | 0 | 0 |
11.S1 | * | 0 | 0 | 0 | 0 | 0 |
12.S2 | * | 0 | 0 | 0 | 0 | 0 |
13.S3 | 0 | * | 0 | 0 | 0 | 0 |
14.S4 | 0 | 0 | * | 0 | 0 | 0 |
Independent context
`T' left context:
`T' right context:
`S' left context: #
`S' right context: #
`A' left context: a , b
`A' right context: a , b , c
`B' left context: a , b , d
`B' right context: a , b
`S1' left context: a
`S1' right context: #
`S2' left context: b
`S2' right context: #
`S3' left context: #
`S3' right context: a
`S4' left context: #
`S4' right context: b
Equivalent definitions:
`A' > 1 & `B' > 1
`A' left context: a , b
`A' right context: a , b , c
`B' left context: a , b , d
`B' right context: a , b
The independent context of `A' and `B' is not different
independent context didn't help us. I'll try to use the dependent one.
I'll find the subsets of dependent context of `A'
gamma3: the source is the production
P=11 `S2' -> `A' b
{b , b}
gamma3: the source is the production
P=10 `S1' -> `A' a
{a , a}
gamma3: the source is the production
P=8 `A' -> `A' c
{a , c} {b , c}
The set of dependent context of `A':
{a , a} {a , c} {b , b} {b , c}
I'll find the subsets of dependent context of `B'
gamma2: the source is the production
P=13 `S4' -> a `B'
{a , b}
gamma2: the source is the production
P=12 `S3' -> b `B'
{b , a}
gamma2: the source is the production
P=9 `B' -> d `B'
{d , a} {d , b}
The set of dependent context of `B':
{a , b} {b , a} {d , a} {d , b}
test_dep_con A and B
dependent context of `A' and `B' is different
Grammar G9.grm is BRC(1,1)-reducible
Dependent context
dependent context of `A':
{a , a} {a , c} {b , b} {b , c}
dependent context of `B':
{a , b} {b , a} {d , a} {d , b}
Semantics
Semantics file is G9.sem
#=1
a=2
b=3
1=4
c=5
d=6
P1=7 $P 1: `T' -> # `S' #
P2=8 $P 2: `S' -> a `S1'
P3=9 $P 3: `S' -> b `S2'
P4=10 $P 4: `S' -> `S4' b
P5=11 $P 5: `S' -> `S3' a
P6=12 $P 6: `A' -> 1
P7=13 $P 7: `B' -> 1
P8=14 $P 8: `A' -> `A' c
P9=15 $P 9: `B' -> d `B'
P10=16 $P10: `S1' -> `A' a
P11=17 $P11: `S2' -> `A' b
P12=18 $P12: `S3' -> b `B'
P13=19 $P13: `S4' -> a `B'
Result tables
File | Size |
G9.prm | 28 |
G9.pm | 225 |
G9.t | 300 |
G9.tt | 140 |
G9.ht | 1540 |
G9.sm | 84 |
G9.v | 808 |
G9.lc | 225 |
G9.rc | 225 |
G9.dc | 215 |
Look at result tablesFinish of CONSTRUCTOR Sat Apr 03 15:57:14 2004