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Added ch. 8 bubblesort exercise & ch. 9 exercises. #19
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,93 @@ | ||
| MODULE main | ||
| VAR | ||
| arr: array 0..4 of 1..5; | ||
| swapped: boolean; | ||
| i: 0..4; | ||
| pc: 1..7; | ||
|
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||
| ASSIGN | ||
| init(arr[0]) := 4; | ||
| init(arr[1]) := 1; | ||
| init(arr[2]) := 3; | ||
| init(arr[3]) := 2; | ||
| init(arr[4]) := 5; | ||
| init(pc) := 2; | ||
| init(i) := 0; | ||
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||
| next(pc) := | ||
| case | ||
| pc=1 & swapped: 2; | ||
| pc=1: 7; | ||
| pc=2: 3; | ||
| pc=3 & i < 4: 4; | ||
| pc=3: 1; | ||
| -- pc=4 & i=0 & arr[i - 1] > arr[i]: 5; | ||
| pc=4 & i=1 & arr[0] > arr[1]: 5; | ||
| pc=4 & i=2 & arr[1] > arr[2]: 5; | ||
| pc=4 & i=3 & arr[2] > arr[3]: 5; | ||
| pc=4 & i=4 & arr[3] > arr[4]: 5; | ||
| pc=4: 3; | ||
| pc=5: 6; | ||
| pc=6: 3; | ||
| pc=7: 7; | ||
| esac; | ||
|
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||
| next(swapped) := | ||
| case | ||
| pc=2: FALSE; | ||
| pc=6: TRUE; | ||
| TRUE: swapped; | ||
| esac; | ||
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||
| next(i) := | ||
| case | ||
| pc=3 & i=0: 1; | ||
| pc=3 & i=1: 2; | ||
| pc=3 & i=2: 3; | ||
| pc=3 & i=3: 4; | ||
| pc=3 & i=4: 0; | ||
| TRUE: i; | ||
| esac; | ||
|
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||
| next(arr[0]) := | ||
| case | ||
| -- pc=5 & i=0: arr[0 - 1]; | ||
| pc=5 & i=1: arr[1]; | ||
| TRUE: arr[0]; | ||
| esac; | ||
| next(arr[1]) := | ||
| case | ||
| pc=5 & i=1: arr[0]; | ||
| pc=5 & i=2: arr[2]; | ||
| TRUE: arr[1]; | ||
| esac; | ||
| next(arr[2]) := | ||
| case | ||
| pc=5 & i=2: arr[1]; | ||
| pc=5 & i=3: arr[3]; | ||
| TRUE: arr[2]; | ||
| esac; | ||
| next(arr[3]) := | ||
| case | ||
| pc=5 & i=3: arr[2]; | ||
| pc=5 & i=4: arr[4]; | ||
| TRUE: arr[3]; | ||
| esac; | ||
| next(arr[4]) := | ||
| case | ||
| pc=5 & i=4: arr[3]; | ||
| -- pc=5 & i=5: arr[4 + 1]; | ||
| TRUE: arr[4]; | ||
| esac; | ||
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||
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| LTLSPEC !F(G(pc=7)) -- the program ends (does not go in loop pc=7) | ||
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||
| LTLSPEC !(F( | ||
| arr[0] = 1 & | ||
| arr[1] = 2 & | ||
| arr[2] = 3 & | ||
| arr[3] = 4 & | ||
| arr[4] = 5 & | ||
| pc = 7 | ||
| ) & (F(G(pc=7)))) -- not (the program loops in pc=7 with a sorted array) |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,111 @@ | ||
| MODULE main | ||
| VAR | ||
| -- the man and the three items | ||
| fox : {right,left}; | ||
| chicken : {right,left}; | ||
| caterpillar : {right,left}; | ||
| lettuce : {right,left}; | ||
| man : {right,left}; | ||
| -- possible moves | ||
| move : {f, c, t, l, e}; | ||
|
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||
| DEFINE | ||
| carry_fox := move=f; | ||
| carry_chicken := move=c; | ||
| carry_caterpillar := move=t; | ||
| carry_lettuce := move=l; | ||
| no_carry := move=e; | ||
|
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||
| ASSIGN | ||
| init(fox) := right; | ||
| init(chicken) := right; | ||
| init(caterpillar) := right; | ||
| init(lettuce) := right; | ||
| init(man) := right; | ||
|
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||
| init(move) := {f, c, t, l, e}; | ||
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||
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||
| TRANS | ||
| next(man) != next(fox) -> next(move) != f | ||
| TRANS | ||
| next(man) != next(chicken) -> next(move) != c | ||
| TRANS | ||
| next(man) != next(caterpillar) -> next(move) != t | ||
| TRANS | ||
| next(man) != next(lettuce) -> next(move) != l | ||
|
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||
| TRANS | ||
| carry_fox -> ( | ||
| next(man) != man & | ||
| next(fox) != fox & | ||
| next(chicken) = chicken & | ||
| next(caterpillar) = caterpillar & | ||
| next(lettuce) = lettuce | ||
| ) | ||
| TRANS | ||
| carry_chicken -> ( | ||
| next(man) != man & | ||
| next(chicken) != chicken & | ||
| next(fox) = fox & | ||
| next(caterpillar) = caterpillar & | ||
| next(lettuce) = lettuce | ||
| ) | ||
| TRANS | ||
| carry_caterpillar -> ( | ||
| next(man) != man & | ||
| next(caterpillar) != caterpillar & | ||
| next(fox) = fox & | ||
| next(chicken) = chicken & | ||
| next(lettuce) = lettuce | ||
| ) | ||
| TRANS | ||
| carry_lettuce -> ( | ||
| next(man) != man & | ||
| next(lettuce) != lettuce & | ||
| next(fox) = fox & | ||
| next(chicken) = chicken & | ||
| next(caterpillar) = caterpillar | ||
| ) | ||
| TRANS | ||
| no_carry -> ( | ||
| next(man) != man & | ||
| next(lettuce) = lettuce & | ||
| next(fox) = fox & | ||
| next(chicken) = chicken & | ||
| next(caterpillar) = caterpillar | ||
| ) | ||
|
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||
| INVAR | ||
| (fox = chicken | chicken = caterpillar) -> chicken = man | ||
| INVAR | ||
| (chicken = caterpillar | caterpillar = lettuce) -> caterpillar = man | ||
|
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| DEFINE | ||
| goal := fox = left & | ||
| chicken = left & | ||
| caterpillar = left & | ||
| lettuce = left; | ||
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| CTLSPEC !EF goal | ||
| CTLSPEC EF goal | ||
|
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||
| -- how come they both are true? | ||
| -- nuXmv > check_ltlspec | ||
| -- specification !( F goal) is true | ||
| -- specification F goal is true | ||
| -- i am so confused | ||
|
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||
| -- nuXmv > check_ctlspec | ||
| --******** WARNING ******** | ||
| --Fair states set of the finite state machine is empty. | ||
| --This might make results of model checking not trustable. | ||
| --******** END WARNING ******** | ||
| -- specification !(EF goal) is true | ||
| --******** WARNING ******** | ||
| --Fair states set of the finite state machine is empty. | ||
| --This might make results of model checking not trustable. | ||
| --******** END WARNING ******** | ||
| -- specification EF goal is true | ||
|
|
||
| -- more confusion | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,123 @@ | ||
| MODULE main | ||
| VAR | ||
| d1 : {left,middle,right}; -- smallest | ||
| d2 : {left,middle,right}; | ||
| d3 : {left,middle,right}; | ||
| d4 : {left,middle,right}; | ||
| d5 : {left,middle,right}; -- largest | ||
| move : 1..5; -- possible moves | ||
|
|
||
| DEFINE | ||
| move_d1 := move=1; | ||
| move_d2 := move=2; | ||
| move_d3 := move=3; | ||
| move_d4 := move=4; | ||
| move_d5 := move=5; | ||
|
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||
| -- di is clear iff it can move to a different pole | ||
| clear_d1 := TRUE; | ||
|
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||
| clear_d2 := d2!=d1; | ||
| clear_d3 := d3!=d1 & d3!=d2; | ||
| clear_d4 := d4!=d1 & d4!=d2 & d4!=d3; | ||
| clear_d5 := d5!=d1 & d5!=d2 & d5!=d3 & d5!=d4; | ||
|
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||
| -- initially all items are on the left pole | ||
| INIT | ||
| d1 = left & | ||
| d2 = left & | ||
| d3 = left & | ||
| d4 = left & | ||
| d5 = left & move = 1; | ||
|
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||
| TRANS | ||
| (next(clear_d3) = FALSE) -> (next(move) != 3) | ||
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||
| TRANS | ||
| (next(clear_d2) = FALSE) -> (next(move) != 2) | ||
|
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||
| TRANS | ||
| (next(clear_d1) = FALSE) -> (next(move) != 1) | ||
|
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||
| TRANS | ||
| (next(clear_d4) = FALSE) -> (next(move) != 4) | ||
|
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||
| TRANS | ||
| (next(clear_d5) = FALSE) -> (next(move) != 5) | ||
|
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||
| TRANS | ||
| move_d1 -> | ||
| next(d1) != d1 & | ||
| next(d2) = d2 & | ||
| next(d3) = d3 & | ||
| next(d4) = d4 & | ||
| next(d5) = d5 | ||
|
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||
| TRANS | ||
| move_d2 -> | ||
| next(d1) = d1 & | ||
| next(d2) != d2 & | ||
| next(d3) = d3 & | ||
| next(d4) = d4 & | ||
| next(d5) = d5 & | ||
| next(d2) != d1 | ||
|
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||
| TRANS | ||
| move_d3 -> | ||
| next(d1) = d1 & | ||
| next(d2) = d2 & | ||
| next(d3) != d3 & | ||
| next(d4) = d4 & | ||
| next(d5) = d5 & | ||
| next(d3) != d1 & | ||
| next(d3) != d2 | ||
|
|
||
| TRANS | ||
| move_d4 -> | ||
| next(d1) = d1 & | ||
| next(d2) = d2 & | ||
| next(d3) = d3 & | ||
| next(d5) = d5 & | ||
| next(d4) != d4 & | ||
| next(d4) != d1 & | ||
| next(d4) != d2 & | ||
| next(d4) != d3 | ||
|
|
||
| TRANS | ||
| move_d5 -> | ||
| next(d1) = d1 & | ||
| next(d2) = d2 & | ||
| next(d3) = d3 & | ||
| next(d4) = d4 & | ||
| next(d5) != d5 & | ||
| next(d5) != d4 & | ||
| next(d5) != d1 & | ||
| next(d5) != d2 & | ||
| next(d5) != d3 | ||
|
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||
| TRANS | ||
| (next(clear_d1) & next(clear_d2) & next(clear_d3)) -> next(move) != 3 | ||
| TRANS | ||
| (next(clear_d1) & next(clear_d2) & next(clear_d4)) -> next(move) != 4 | ||
| TRANS | ||
| (next(clear_d1) & next(clear_d2) & next(clear_d5)) -> next(move) != 5 | ||
| TRANS | ||
| (next(clear_d1) & next(clear_d3) & next(clear_d4)) -> next(move) != 4 | ||
| TRANS | ||
| (next(clear_d1) & next(clear_d3) & next(clear_d5)) -> next(move) != 5 | ||
| TRANS | ||
| (next(clear_d1) & next(clear_d4) & next(clear_d5)) -> next(move) != 5 | ||
| TRANS | ||
| (next(clear_d2) & next(clear_d3) & next(clear_d4)) -> next(move) != 4 | ||
| TRANS | ||
| (next(clear_d2) & next(clear_d3) & next(clear_d5)) -> next(move) != 5 | ||
| TRANS | ||
| (next(clear_d2) & next(clear_d4) & next(clear_d5)) -> next(move) != 5 | ||
| TRANS | ||
| (next(clear_d3) & next(clear_d4) & next(clear_d5)) -> next(move) != 5 | ||
|
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||
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||
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| -- spec to find a solution to the problem | ||
| LTLSPEC | ||
| ! F(d1=right & d2=right & d3=right & d4=right & d5=right) |
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