Start of CONSTRUCTOR for the Grammar G100.grm Sat Apr 03 15:40:39 2004
Terminal alphabet
# 1 = #
# 2 = a
# 3 = b
# 4 = 0
# 5 = 1
Nonterminal alphabet
# 6 = `T'
# 7 = `S'
# 8 = `A'
# 9 = `B'
#10 = `C'
#11 = `D'
Productions
P 1: `T' -> # `S' #
P 2: `S' -> a `A'
P 3: `S' -> b `B'
P 4: `A' -> 0 `A' 1
P 5: `A' -> 0 1
P 6: `B' -> `C' 1
P 7: `C' -> 0 `B' 1
P 8: `B' -> `D' 1
P 9: `D' -> 0 1
Leftmost-set
Symbol | # | a | b | 0 | 1 | T | S | A | B | C | D |
6.T | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
7.S | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8.A | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
9.B | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | * | * |
10.C | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
11.D | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Rightmost-set
Symbol | # | a | b | 0 | 1 | T | S | A | B | C | D |
6.T | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
7.S | 0 | 0 | 0 | 0 | * | 0 | 0 | * | * | 0 | 0 |
8.A | 0 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 |
9.B | 0 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 |
10.C | 0 | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 |
11.D | 0 | 0 | 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: 1 , A , B
`A' leftmost set: `0'
`A' rightmost set: 1
`B' leftmost set: `0' , `C' , `D'
`B' rightmost set: 1
`C' leftmost set: `0'
`C' rightmost set: 1
`D' leftmost set: `0'
`D' rightmost set: 1
Precedence matrix
Symbol | # | a | b | 0 | 1 | T | S | A | B | C | D |
1.# | 0 | < | < | 0 | 0 | 0 | = | 0 | 0 | 0 | 0 |
2.a | 0 | 0 | 0 | < | 0 | 0 | 0 | = | 0 | 0 | 0 |
3.b | 0 | 0 | 0 | < | 0 | 0 | 0 | 0 | = | < | < |
4.0 | 0 | 0 | 0 | < | = | 0 | 0 | = | = | < | < |
5.1 | > | 0 | 0 | 0 | > | 0 | 0 | 0 | 0 | 0 | 0 |
6.T | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
7.S | = | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8.A | > | 0 | 0 | 0 | = | 0 | 0 | 0 | 0 | 0 | 0 |
9.B | > | 0 | 0 | 0 | = | 0 | 0 | 0 | 0 | 0 | 0 |
10.C | 0 | 0 | 0 | 0 | = | 0 | 0 | 0 | 0 | 0 | 0 |
11.D | 0 | 0 | 0 | 0 | = | 0 | 0 | 0 | 0 | 0 | 0 |
The relationships of symbol #1 #:
The relationships of symbol #2 a:
The relationships of symbol #3 b:
< 0 | = `B' | < `C' | < `D' |
The relationships of symbol #4 0:
< 0 | = 1 | = `A' | = `B' | < `C' | < `D' |
The relationships of symbol #5 1:
The relationships of symbol #6 `T':
The relationships of symbol #7 `S':
The relationships of symbol #8 `A':
The relationships of symbol #9 `B':
The relationships of symbol #10 `C':
The relationships of symbol #11 `D':
Grammar G100.grm is a precedence grammar
Grammar G100.grm is not invertible
Left Context
Symbol | # | a | b | 0 | 1 | T | S | A | B | C | D |
6.T | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
7.S | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8.A | 0 | * | 0 | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
9.B | 0 | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
10.C | 0 | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
11.D | 0 | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Right Context
Symbol | # | a | b | 0 | 1 |
6.T | 0 | 0 | 0 | 0 | 0 |
7.S | * | 0 | 0 | 0 | 0 |
8.A | * | 0 | 0 | 0 | * |
9.B | * | 0 | 0 | 0 | * |
10.C | 0 | 0 | 0 | 0 | * |
11.D | 0 | 0 | 0 | 0 | * |
Independent context
`T' left context:
`T' right context:
`S' left context: #
`S' right context: #
`A' left context: a , 0
`A' right context: # , 1
`B' left context: b , 0
`B' right context: # , 1
`C' left context: b , 0
`C' right context: 1
`D' left context: b , 0
`D' right context: 1
Equivalent definitions:
`A' > 0 1 & `D' > 0 1
`A' left context: a , 0
`A' right context: # , 1
`D' left context: b , 0
`D' right context: 1
The independent context of `A' and `D' 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'
gamma1: the source is the production
P=4 `A' -> 0 `A' 1
{0 , 1}
gamma2: the source is the production
P=2 `S' -> a `A'
{a , #}
The set of dependent context of `A':
{a , #} {0 , 1}
I'll find the subsets of dependent context of `D'
gamma3: the source is the production
P=8 `B' -> `D' 1
{b , 1} {0 , 1}
The set of dependent context of `D':
{b , 1} {0 , 1}
test_dep_con A and D
common: {0 , 1}
dependent context is not different: A and D
Grammar G100.grm is not BRC-reducible
The following pairs of nonterminals are having nondifferent context:
`A'and `D'
Finish of CONSTRUCTOR Sat Apr 03 15:40:39 2004