Start of CONSTRUCTOR for the Grammar G26.grm Sat Apr 03 15:48:30 2004
Terminal alphabet
# 1 = #
# 2 = a
# 3 = b
# 4 = 1
# 5 = c
Nonterminal alphabet
# 6 = `T'
# 7 = `S'
# 8 = `A'
# 9 = `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' -> c `B' c
Leftmost-set
| Symbol | # | a | b | 1 | c | T | S | A | B |
| 6.T | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7.S | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 |
| 8.A | 0 | 0 | 0 | * | * | 0 | 0 | 0 | 0 |
| 9.B | 0 | 0 | 0 | * | 0 | 0 | 0 | 0 | 0 |
Rightmost-set
| Symbol | # | a | b | 1 | c | T | S | A | B |
| 6.T | * | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7.S | 0 | * | * | 0 | 0 | 0 | 0 | 0 | 0 |
| 8.A | 0 | 0 | 0 | * | * | 0 | 0 | 0 | 0 |
| 9.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' , `c'
`A' rightmost set: 1 , c
`B' leftmost set: `1'
`B' rightmost set: 1
Precedence matrix
| Symbol | # | a | b | 1 | c | T | S | A | B |
| 1.# | 0 | < | < | 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.c | 0 | > | > | < | 0 | 0 | 0 | 0 | = |
| 6.T | 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 |
| 9.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 c:
The relationships of symbol #6 `T':
The relationships of symbol #7 `S':
The relationships of symbol #8 `A':
The relationships of symbol #9 `B':
Grammar G26.grm is a precedence grammar
Grammar G26.grm is not invertible
Left Context
| Symbol | # | a | b | 1 | c | T | S | A | B |
| 6.T | 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 |
| 9.B | 0 | * | * | 0 | * | 0 | 0 | 0 | 0 |
Right Context
| Symbol | # | a | b | 1 | c |
| 6.T | 0 | 0 | 0 | 0 | 0 |
| 7.S | * | 0 | 0 | 0 | 0 |
| 8.A | 0 | * | * | 0 | 0 |
| 9.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 , c
`B' right context: a , b , c
Equivalent definitions:
`A' —> 1 & `B' —> 1
`A' left context: a , b
`A' right context: a , b
`B' left context: a , b , c
`B' right context: a , b , c
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}
gamma1: the source is the production
P=8 `A' -> c `B' c
{c , c}
The set of dependent context of `B':
{a , b} {b , a} {c , c}
test_dep_con A and B
dependent context of `A' and `B' is different
Grammar G26.grm is BRC(1,1)-reducible
Dependent context
dependent context of `A':
{a , a} {b , b}
dependent context of `B':
{a , b} {b , a} {c , c}
Semantics
Semantics file is G26.sem
p=15 piir=15
p=16 piir=15
#=1
a=2
b=3
1=4
c=5
P1=7 $P 1: `T' -> # `S' #
P2=8 $P 2: `S' -> a `A' a
P3=9 $P 3: `S' -> b `A' b
P4=10 $P 4: `S' -> a `B' b
P5=11 $P 5: `S' -> b `B' a
P6=12 $P 6: `A' -> 1
P7=13 $P 7: `B' -> 1
P8=14 $P 8: `A' -> c `B' c
P9=15 $
Result tables
| File | Size |
| G26.prm | 28 |
| G26.pm | 100 |
| G26.t | 200 |
| G26.tt | 120 |
| G26.ht | 1360 |
| G26.sm | 60 |
| G26.v | 528 |
| G26.lc | 100 |
| G26.rc | 100 |
| G26.dc | 150 |
Look at result tablesFinish of CONSTRUCTOR Sat Apr 03 15:48:30 2004