From e3cadac9a77a7f635e3e8c4ca8258b3f7fa5e3b2 Mon Sep 17 00:00:00 2001 From: sp Date: Mon, 27 May 2024 22:17:26 +0200 Subject: [PATCH] update for lecture 3 --- Lecture3/colours.py | 28 ++++++++++++++ Lecture3/equality.py | 35 +++++++++++++++++ Lecture3/example_quantifier.py | 9 +++++ Lecture3/example_unsat_core.py | 9 +++++ Lecture3/snippet.py | 57 ++++++++++++++++++++++++++++ Lecture_05b_SS24_Z3_intro_contd.pdf | Bin 665081 -> 0 bytes 6 files changed, 138 insertions(+) create mode 100644 Lecture3/colours.py create mode 100644 Lecture3/equality.py create mode 100644 Lecture3/example_quantifier.py create mode 100644 Lecture3/example_unsat_core.py create mode 100644 Lecture3/snippet.py delete mode 100644 Lecture_05b_SS24_Z3_intro_contd.pdf diff --git a/Lecture3/colours.py b/Lecture3/colours.py new file mode 100644 index 0000000..1e0122b --- /dev/null +++ b/Lecture3/colours.py @@ -0,0 +1,28 @@ +from itertools import combinations +from z3 import * + +solver = Solver() + +Colours = Datatype("Colours") +Colours.declare("RED") +Colours.declare("BLUE") +Colours.declare("GREEN") +Colours.declare("YELLOW") + +Colour = Colours.create() +f = Function('f', IntSort(), Colour) + +variables = list() +for i in range(0,5): + variables.append(Int(i)) + solver.add(0 <= variables[-1]) + solver.add(variables[-1] <= 5) + +solver.add(Distinct(variables)) + +for combi in combinations(variables,2): + solver.add(Implies(Abs(combi[0] - combi[1]) == 1, f(combi[0]) != f(combi[1]))) + +result = solver.check() +if result == sat: + print(solver.model()) diff --git a/Lecture3/equality.py b/Lecture3/equality.py new file mode 100644 index 0000000..05ffe16 --- /dev/null +++ b/Lecture3/equality.py @@ -0,0 +1,35 @@ +from z3 import * +s = Solver() +bv_size = 4 +a, b = BitVecs('a b', bv_size) +x = BitVec('x', bv_size) +lhs,rhs = BitVecs('lhs rhs', bv_size) + + +s.add(lhs == ((x+a)^b)-a) +s.add(rhs == ((x-a)^b)+a) +s.push() +s.add(ForAll(x, lhs == rhs)) +# enumerate all possible solutions: +results=[] +while True: + if s.check() == sat: + m = s.model() + print (m) + results.append(m) + block = [] + block = [a != m[a].as_long(), b != m[b].as_long()] + s.add(Or(block)) + else: + print ("results total=", len(results)) + break +#print(s.sexpr()) + +s.pop() +s.add(Exists(x, lhs != rhs)) +result = s.check() +print(result) +if result == sat: + print(f"Example where lhs != rhs: {s.model()}") + + diff --git a/Lecture3/example_quantifier.py b/Lecture3/example_quantifier.py new file mode 100644 index 0000000..4e81785 --- /dev/null +++ b/Lecture3/example_quantifier.py @@ -0,0 +1,9 @@ +from z3 import * + +x, y = Ints("x y") + +solver = Solver() +# Check if for all x and y, s.t. if x < 0 and y < 0, x + y < 0 + +result = solver.check() +print(result) diff --git a/Lecture3/example_unsat_core.py b/Lecture3/example_unsat_core.py new file mode 100644 index 0000000..fcc772f --- /dev/null +++ b/Lecture3/example_unsat_core.py @@ -0,0 +1,9 @@ +from z3 import * + +p, q = Bools('p q') +s = Solver() +s.add(Not(q)) +s.assert_and_track(q, "p1") +s.assert_and_track(p, "p2") +print(s.check()) +print(s.unsat_core()) diff --git a/Lecture3/snippet.py b/Lecture3/snippet.py new file mode 100644 index 0000000..0e0d1eb --- /dev/null +++ b/Lecture3/snippet.py @@ -0,0 +1,57 @@ +solver = z3.Solver() + +num = len(matching) +goal_steps = [[z3.Int(f'g-{n}-{t}') for t in range(num+1)] for n in range(num)] # goal number-of-match time +goal_steps_bool = [[z3.Bool(f'gb-{n}-{t}') for t in range(num+1)] for n in range(num)] +start_steps = [[z3.Int(f's-{n}-{t}') for t in range(num+1)] for n in range(num)] # start number-of-match time +start_steps_bool = [[z3.Bool(f'sb-{n}-{t}') for t in range(num+1)] for n in range(num)] + +for n in range(num): +for t in range(num+1): + solver.add(z3.Or(start_steps[n][t]==0,start_steps[n][t]==1)) + solver.add(z3.Or(goal_steps[n][t]==0,goal_steps[n][t]==1)) + + # start and end always different + solver.add(start_steps[n][t] != goal_steps[n][t]) + + solver.add(goal_steps_bool[n][t] == z3.If(goal_steps[n][t]==1,True,False)) + solver.add(goal_steps[n][t] == z3.If(goal_steps_bool[n][t]==True,1,0)) + solver.add(start_steps_bool[n][t] == z3.If(start_steps[n][t]==1,True,False)) + solver.add(start_steps[n][t] == z3.If(start_steps_bool[n][t]==True,1,0)) + +for t in range(num+1): + solver.add(z3.Sum([goal_steps[ni][t] for ni in range(num)]) == t) # at t=0, all goals false -> increasing + +# given implicitly, s != g +# starts_at_t = [start_steps[ni][t] for ni in range(num)] +# solver.add(z3.Sum(starts_at_t) == (num-t)) # at t=0, all start + +for n in range(num): + for t in range(num+1): + solver.add(z3.Implies(goal_steps_bool[n][t],z3.And(goal_steps_bool[n][t+1:num+1]))) + +for s_pt,_,g_vec in start_intersect_triple: + s_pt_i = find_index_init(matching,s_pt) + g_vec_i = find_index_goal(matching,g_vec) + conflicting_starts = [] + for t in range(num+1): + conflicting_starts.append(z3.Implies( goal_steps_bool[g_vec_i][t],z3.Or( [z3.Not(start_steps_bool[s_pt_i][ti]) for ti in range(t)] ) )) + solver.assert_and_track(z3.And(conflicting_starts), f"s-i1:{s_pt_i};i2:{g_vec_i}") + +for g_pt,_,g_vec in goal_intersect_triple: + g_pt_i = find_index_goal(matching,g_pt) + g_vec_i = find_index_goal(matching,g_vec) + conflicting_goals = [] + for t in range(num+1): + conflicting_goals.append(z3.Implies( goal_steps_bool[g_pt_i][t], z3.Or([goal_steps_bool[g_vec_i][ti] for ti in range(t)]) )) + solver.assert_and_track(z3.And(conflicting_goals),f"g-i1:{g_pt_i};i2:{g_vec_i}") + + +res = solver.check() +if res == z3.sat: + print(solver.model()) +else: + core = solver.unsat_core() + print(solver.sexpr()) + print(core) + diff --git a/Lecture_05b_SS24_Z3_intro_contd.pdf b/Lecture_05b_SS24_Z3_intro_contd.pdf deleted file mode 100644 index 81cbcb3b767a86d2a34ea8a3fcdedbe97a9f6af1..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 665081 zcmce-byQr 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