Start of CONSTRUCTOR for the Grammar G8.grm Sat Apr 03 15:56:08 2004
Terminal alphabet
# 1 = #
# 2 = a
# 3 = b
# 4 = 1
Nonterminal alphabet
# 5 = `T'
# 6 = `S'
# 7 = `A'
# 8 = `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
Leftmost-set
| Symbol | # | a | b | 1 | T | S | A | B |
| 5.T | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 6.S | 0 | * | * | 0 | 0 | 0 | 0 | 0 |
| 7.A | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 |
| 8.B | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 |
Rightmost-set
| Symbol | # | a | b | 1 | T | S | A | B |
| 5.T | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 6.S | 0 | * | * | 0 | 0 | 0 | 0 | 0 |
| 7.A | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 |
| 8.B | 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' rightmost set: 1
`B' leftmost set: `1'
`B' rightmost set: 1
Precedence matrix
| Symbol | # | a | b | 1 | T | S | A | B |
| 1.# | 0 | < | < | 0 | 0 | = | 0 | 0 |
| 2.a | > | 0 | 0 | < | 0 | 0 | = | = |
| 3.b | > | 0 | 0 | < | 0 | 0 | = | = |
| 4.1 | 0 | > | > | 0 | 0 | 0 | 0 | 0 |
| 5.T | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 6.S | = | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7.A | 0 | = | = | 0 | 0 | 0 | 0 | 0 |
| 8.B | 0 | = | = | 0 | 0 | 0 | 0 | 0 |
The relationships of symbol #1 #:
The relationships of symbol #2 a:
The relationships of symbol #3 b:
The relationships of symbol #4 1:
The relationships of symbol #5 `T':
The relationships of symbol #6 `S':
The relationships of symbol #7 `A':
The relationships of symbol #8 `B':
Grammar G8.grm is a precedence grammar
Grammar G8.grm is not invertible
Left Context
| Symbol | # | a | b | 1 | T | S | A | B |
| 5.T | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 6.S | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7.A | 0 | * | * | 0 | 0 | 0 | 0 | 0 |
| 8.B | 0 | * | * | 0 | 0 | 0 | 0 | 0 |
Right Context
| Symbol | # | a | b | 1 |
| 5.T | 0 | 0 | 0 | 0 |
| 6.S | * | 0 | 0 | 0 |
| 7.A | 0 | * | * | 0 |
| 8.B | 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
`B' left context: a , b
`B' right context: a , b
Equivalent definitions:
`A' —> 1 & `B' —> 1
`A' left context: a , b
`A' right context: a , b
`B' left context: a , b
`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'
gamma1: the source is the production
P=2 `S' -> a `A' a
{a , a}
gamma1: the source is the production
P=3 `S' -> b `A' b
{b , b}
The set of dependent context of `A':
{a , a} {b , b}
I'll find the subsets of dependent context of `B'
gamma1: the source is the production
P=4 `S' -> a `B' b
{a , b}
gamma1: the source is the production
P=5 `S' -> b `B' a
{b , a}
The set of dependent context of `B':
{a , b} {b , a}
test_dep_con A and B
dependent context of `A' and `B' is different
Grammar G8.grm is BRC(1,1)-reducible
Dependent context
dependent context of `A':
{a , a} {b , b}
dependent context of `B':
{a , b} {b , a}
Semantics
Semantics file is G8.sem
#=1
a=2
b=3
1=4
P1=5 $P 1: `T' -> # `S' #
P2=6 $P 2: `S' -> a `A' a
P3=7 $P 3: `S' -> b `A' b
P4=8 $P 4: `S' -> a `B' b
P5=9 $P 5: `S' -> b `B' a
P6=10 $P 6: `A' -> 1
P7=11 $P 7: `B' -> 1
Result tables
| File | Size |
| G8.prm | 28 |
| G8.pm | 81 |
| G8.t | 180 |
| G8.tt | 100 |
| G8.ht | 1316 |
| G8.sm | 52 |
| G8.v | 464 |
| G8.lc | 81 |
| G8.rc | 81 |
| G8.dc | 128 |
Look at result tablesFinish of CONSTRUCTOR Sat Apr 03 15:56:08 2004