Normal form of formula returned by Z3's qe tactic
I'm using Z3's quantifier elimination tactic via Z3py and have tried the following examples.
from z3 import *
x,y,xp,yp = Ints('x y xp yp')
t = Tactic('qe')
t(Exists((xp, yp), And(xp==x+1, yp==y+2, xp<=8, xp >=1, yp<=12, yp>=2)))
#returns: [[y <= 10, y >= 0, x <= 7, x >= 0]]
t(Exists((xp, yp), Implies(x<10 , And(xp==x+1, yp==y+2, xp<=8, xp >=1, yp<=12, yp>=2))))
#returns: [[Or(10 <= x, And(y <= 10, y >= 0, And(x <= 7, x >= 0)))]]
I think that the resultant formulas are in quantifier-free DNF(which is what I need), but I could not find anything in the API documentation that guarantees it. Does anyone know if qe always returns formulas in DNF?
Where can I(if at all) find such details regarding tactics without having to dig through the original source code?
EDIT: All formulas are restricted to linear integer arithmetic.
z3 smt z3py quantifiers
asked Nov 11 '18 at 7:09
AkayAkay
1375
add a comment |
I'm using Z3's quantifier elimination tactic via Z3py and have tried the following examples.
from z3 import *
x,y,xp,yp = Ints('x y xp yp')
t = Tactic('qe')
t(Exists((xp, yp), And(xp==x+1, yp==y+2, xp<=8, xp >=1, yp<=12, yp>=2)))
#returns: [[y <= 10, y >= 0, x <= 7, x >= 0]]
t(Exists((xp, yp), Implies(x<10 , And(xp==x+1, yp==y+2, xp<=8, xp >=1, yp<=12, yp>=2))))
#returns: [[Or(10 <= x, And(y <= 10, y >= 0, And(x <= 7, x >= 0)))]]
I think that the resultant formulas are in quantifier-free DNF(which is what I need), but I could not find anything in the API documentation that guarantees it. Does anyone know if qe always returns formulas in DNF?
Where can I(if at all) find such details regarding tactics without having to dig through the original source code?
EDIT: All formulas are restricted to linear integer arithmetic.
z3 smt z3py quantifiers
asked Nov 11 '18 at 7:09
AkayAkay
1375
add a comment |
I'm using Z3's quantifier elimination tactic via Z3py and have tried the following examples.
from z3 import *
x,y,xp,yp = Ints('x y xp yp')
t = Tactic('qe')
t(Exists((xp, yp), And(xp==x+1, yp==y+2, xp<=8, xp >=1, yp<=12, yp>=2)))
#returns: [[y <= 10, y >= 0, x <= 7, x >= 0]]
t(Exists((xp, yp), Implies(x<10 , And(xp==x+1, yp==y+2, xp<=8, xp >=1, yp<=12, yp>=2))))
#returns: [[Or(10 <= x, And(y <= 10, y >= 0, And(x <= 7, x >= 0)))]]
I think that the resultant formulas are in quantifier-free DNF(which is what I need), but I could not find anything in the API documentation that guarantees it. Does anyone know if qe always returns formulas in DNF?
Where can I(if at all) find such details regarding tactics without having to dig through the original source code?
EDIT: All formulas are restricted to linear integer arithmetic.
z3 smt z3py quantifiers
asked Nov 11 '18 at 7:09
AkayAkay
1375
I'm using Z3's quantifier elimination tactic via Z3py and have tried the following examples.
from z3 import *
x,y,xp,yp = Ints('x y xp yp')
t = Tactic('qe')
t(Exists((xp, yp), And(xp==x+1, yp==y+2, xp<=8, xp >=1, yp<=12, yp>=2)))
#returns: [[y <= 10, y >= 0, x <= 7, x >= 0]]
t(Exists((xp, yp), Implies(x<10 , And(xp==x+1, yp==y+2, xp<=8, xp >=1, yp<=12, yp>=2))))
#returns: [[Or(10 <= x, And(y <= 10, y >= 0, And(x <= 7, x >= 0)))]]
I think that the resultant formulas are in quantifier-free DNF(which is what I need), but I could not find anything in the API documentation that guarantees it. Does anyone know if qe always returns formulas in DNF?
Where can I(if at all) find such details regarding tactics without having to dig through the original source code?
EDIT: All formulas are restricted to linear integer arithmetic.
z3 smt z3py quantifiers
z3 smt z3py quantifiers
asked Nov 11 '18 at 7:09
AkayAkay
1375
asked Nov 11 '18 at 7:09
AkayAkay
1375
edited Nov 11 '18 at 7:34
Akay
asked Nov 11 '18 at 7:09
AkayAkay
1375
asked Nov 11 '18 at 7:09
AkayAkay
1375
asked Nov 11 '18 at 7:09
AkayAkay
1375
1375
add a comment |
add a comment |
1 Answer
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By design, tactics make "best effort." That is, while qe is designed to eliminate quantifiers, it may end up failing to do so, returning the goal stack unchanged.
Note that quantifier elimination is not just one tactic, but it is a whole collection of them, depending on what other theories are involved in your benchmark. See the directory: https://github.com/Z3Prover/z3/tree/master/src/qe
answered Nov 11 '18 at 7:31
Levent ErkokLevent Erkok
7,34111027
For my current use case, I have purely linear integer arithmetic formulas. I tried reading the source you linked to, but I'm not at all familiar with Z3's internals. Is there any documentation on this?
– Akay
Nov 11 '18 at 8:38
I doubt there's any direct documentation other than the source code itself. If you're looking for general information on quantifier elimination, then I'm sure you can find many scholarly articles on that.
– Levent Erkok
Nov 11 '18 at 16:15
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
By design, tactics make "best effort." That is, while qe is designed to eliminate quantifiers, it may end up failing to do so, returning the goal stack unchanged.
Note that quantifier elimination is not just one tactic, but it is a whole collection of them, depending on what other theories are involved in your benchmark. See the directory: https://github.com/Z3Prover/z3/tree/master/src/qe
answered Nov 11 '18 at 7:31
Levent ErkokLevent Erkok
7,34111027
For my current use case, I have purely linear integer arithmetic formulas. I tried reading the source you linked to, but I'm not at all familiar with Z3's internals. Is there any documentation on this?
– Akay
Nov 11 '18 at 8:38
I doubt there's any direct documentation other than the source code itself. If you're looking for general information on quantifier elimination, then I'm sure you can find many scholarly articles on that.
– Levent Erkok
Nov 11 '18 at 16:15
add a comment |
By design, tactics make "best effort." That is, while qe is designed to eliminate quantifiers, it may end up failing to do so, returning the goal stack unchanged.
Note that quantifier elimination is not just one tactic, but it is a whole collection of them, depending on what other theories are involved in your benchmark. See the directory: https://github.com/Z3Prover/z3/tree/master/src/qe
answered Nov 11 '18 at 7:31
Levent ErkokLevent Erkok
7,34111027
For my current use case, I have purely linear integer arithmetic formulas. I tried reading the source you linked to, but I'm not at all familiar with Z3's internals. Is there any documentation on this?
– Akay
Nov 11 '18 at 8:38
I doubt there's any direct documentation other than the source code itself. If you're looking for general information on quantifier elimination, then I'm sure you can find many scholarly articles on that.
– Levent Erkok
Nov 11 '18 at 16:15
add a comment |
By design, tactics make "best effort." That is, while qe is designed to eliminate quantifiers, it may end up failing to do so, returning the goal stack unchanged.
Note that quantifier elimination is not just one tactic, but it is a whole collection of them, depending on what other theories are involved in your benchmark. See the directory: https://github.com/Z3Prover/z3/tree/master/src/qe
answered Nov 11 '18 at 7:31
Levent ErkokLevent Erkok
7,34111027
By design, tactics make "best effort." That is, while qe is designed to eliminate quantifiers, it may end up failing to do so, returning the goal stack unchanged.
Note that quantifier elimination is not just one tactic, but it is a whole collection of them, depending on what other theories are involved in your benchmark. See the directory: https://github.com/Z3Prover/z3/tree/master/src/qe
answered Nov 11 '18 at 7:31
Levent ErkokLevent Erkok
7,34111027
answered Nov 11 '18 at 7:31
Levent ErkokLevent Erkok
7,34111027
answered Nov 11 '18 at 7:31
Levent ErkokLevent Erkok
7,34111027
answered Nov 11 '18 at 7:31
Levent ErkokLevent Erkok
7,34111027
7,34111027
For my current use case, I have purely linear integer arithmetic formulas. I tried reading the source you linked to, but I'm not at all familiar with Z3's internals. Is there any documentation on this?
– Akay
Nov 11 '18 at 8:38
I doubt there's any direct documentation other than the source code itself. If you're looking for general information on quantifier elimination, then I'm sure you can find many scholarly articles on that.
– Levent Erkok
Nov 11 '18 at 16:15
add a comment |
For my current use case, I have purely linear integer arithmetic formulas. I tried reading the source you linked to, but I'm not at all familiar with Z3's internals. Is there any documentation on this?
– Akay
Nov 11 '18 at 8:38
I doubt there's any direct documentation other than the source code itself. If you're looking for general information on quantifier elimination, then I'm sure you can find many scholarly articles on that.
– Levent Erkok
Nov 11 '18 at 16:15
For my current use case, I have purely linear integer arithmetic formulas. I tried reading the source you linked to, but I'm not at all familiar with Z3's internals. Is there any documentation on this?
– Akay
Nov 11 '18 at 8:38
For my current use case, I have purely linear integer arithmetic formulas. I tried reading the source you linked to, but I'm not at all familiar with Z3's internals. Is there any documentation on this?
– Akay
Nov 11 '18 at 8:38
I doubt there's any direct documentation other than the source code itself. If you're looking for general information on quantifier elimination, then I'm sure you can find many scholarly articles on that.
– Levent Erkok
Nov 11 '18 at 16:15
I doubt there's any direct documentation other than the source code itself. If you're looking for general information on quantifier elimination, then I'm sure you can find many scholarly articles on that.
– Levent Erkok
Nov 11 '18 at 16:15
add a comment |
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