Example #1
0
def test_quantify():
    ordering = {'x': 0, 'y': 1, 'z': 2}
    g = BDD(ordering)
    # x & y
    e = g.add_expr('x && ! y')
    x = g.add_expr('x')
    not_y = g.add_expr('! y')
    assert g.quantify(e, {'x'}) == not_y
    assert g.quantify(e, {'x'}, forall=True) == -1
    assert g.quantify(e, {'y'}) == x
    assert g.quantify(e, {'x'}, forall=True) == -1
    # x | y | z
    e = g.add_expr('x || y || z')
    xy = g.add_expr('x || y')
    yz = g.add_expr('y || z')
    zx = g.add_expr('z || x')
    assert g.quantify(e, {'x'})
    assert g.quantify(e, {'y'})
    assert g.quantify(e, {'z'})
    assert g.quantify(e, {'z'}, forall=True) == xy
    assert g.quantify(e, {'x'}, forall=True) == yz
    assert g.quantify(e, {'y'}, forall=True) == zx
    # complement edges
    u = -x
    v = g.quantify(u, {'y'}, forall=True)
    assert v == -x, g.to_expr(v)
    # multiple values: test recursion
    e = g.add_expr('x & y & z')
    x = g.add_expr('x')
    r = g.quantify(e, {'y', 'z'})
    assert r == x, r
Example #2
0
def test_quantify():
    ordering = {'x': 0, 'y': 1, 'z': 2}
    g = BDD(ordering)
    # x & y
    e = g.add_expr('x && ! y')
    x = g.add_expr('x')
    not_y = g.add_expr('! y')
    assert g.quantify(e, {'x'}) == not_y
    assert g.quantify(e, {'x'}, forall=True) == -1
    assert g.quantify(e, {'y'}) == x
    assert g.quantify(e, {'x'}, forall=True) == -1
    # x | y | z
    e = g.add_expr('x || y || z')
    xy = g.add_expr('x || y')
    yz = g.add_expr('y || z')
    zx = g.add_expr('z || x')
    assert g.quantify(e, {'x'})
    assert g.quantify(e, {'y'})
    assert g.quantify(e, {'z'})
    assert g.quantify(e, {'z'}, forall=True) == xy
    assert g.quantify(e, {'x'}, forall=True) == yz
    assert g.quantify(e, {'y'}, forall=True) == zx
    # complement edges
    u = -x
    v = g.quantify(u, {'y'}, forall=True)
    assert v == -x, g.to_expr(v)
    # multiple values: test recursion
    e = g.add_expr('x & y & z')
    x = g.add_expr('x')
    r = g.quantify(e, {'y', 'z'})
    assert r == x, r
Example #3
0
def test_preimage():
    # exists: x, y
    # forall: z
    ordering = {'x': 0, 'xp': 1,
                'y': 2, 'yp': 3,
                'z': 4, 'zp': 5}
    rename = {0: 1, 2: 3, 4: 5}
    g = BDD(ordering)
    f = g.add_expr('!x')
    t = g.add_expr('x <-> !xp')
    qvars = {1, 3}
    p = preimage(t, f, rename, qvars, g)
    x = g.add_expr('x')
    assert x == p, (x, p)
    # a cycle
    # (x & y) -> (!x & y) ->
    # (!x & !y) -> (x & !y) -> wrap around
    t = g.add_expr(
        '((x & y) -> (!xp & yp)) && '
        '((!x & y) -> (!xp & !yp)) && '
        '((!x & !y) -> (xp & !yp)) && '
        '((x & !y) -> (xp & yp))')
    f = g.add_expr('x && y')
    p = preimage(t, f, rename, qvars, g)
    assert p == g.add_expr('x & !y')
    f = g.add_expr('x && !y')
    p = preimage(t, f, rename, qvars, g)
    assert p == g.add_expr('!x & !y')
    # backward reachable set
    f = g.add_expr('x & y')
    oldf = None
    while oldf != f:
        p = preimage(t, f, rename, qvars, g)
        oldf = f
        f = g.apply('or', p, oldf)
    assert f == 1
    # go around once
    f = g.add_expr('x & y')
    start = f
    for i in range(4):
        f = preimage(t, f, rename, qvars, g)
    end = f
    assert start == end
    # forall z exists x, y
    t = g.add_expr(
        '('
        '    ((x & y) -> (zp & xp & !yp)) | '
        '    ((x & y) -> (!zp & !xp & yp))'
        ') & '
        '(!(x & y) -> False)')
    f = g.add_expr('x && !y')
    ep = preimage(t, f, rename, qvars, g)
    p = g.quantify(ep, {'zp'}, forall=True)
    assert p == -1
    f = g.add_expr('(x & !y) | (!x & y)')
    ep = preimage(t, f, rename, qvars, g)
    p = g.quantify(ep, {'zp'}, forall=True)
    assert p == g.add_expr('x & y')
Example #4
0
def test_preimage():
    # exists: x, y
    # forall: z
    ordering = {'x': 0, 'xp': 1, 'y': 2, 'yp': 3, 'z': 4, 'zp': 5}
    rename = {0: 1, 2: 3, 4: 5}
    g = BDD(ordering)
    f = g.add_expr('!x')
    t = g.add_expr('x <-> !xp')
    qvars = {1, 3}
    p = preimage(t, f, rename, qvars, g)
    x = g.add_expr('x')
    assert x == p, (x, p)
    # a cycle
    # (x & y) -> (!x & y) ->
    # (!x & !y) -> (x & !y) -> wrap around
    t = g.add_expr('((x & y) -> (!xp & yp)) && '
                   '((!x & y) -> (!xp & !yp)) && '
                   '((!x & !y) -> (xp & !yp)) && '
                   '((x & !y) -> (xp & yp))')
    f = g.add_expr('x && y')
    p = preimage(t, f, rename, qvars, g)
    assert p == g.add_expr('x & !y')
    f = g.add_expr('x && !y')
    p = preimage(t, f, rename, qvars, g)
    assert p == g.add_expr('!x & !y')
    # backward reachable set
    f = g.add_expr('x & y')
    oldf = None
    while oldf != f:
        p = preimage(t, f, rename, qvars, g)
        oldf = f
        f = g.apply('or', p, oldf)
    assert f == 1
    # go around once
    f = g.add_expr('x & y')
    start = f
    for i in xrange(4):
        f = preimage(t, f, rename, qvars, g)
    end = f
    assert start == end
    # forall z exists x, y
    t = g.add_expr('('
                   '    ((x & y) -> (zp & xp & !yp)) | '
                   '    ((x & y) -> (!zp & !xp & yp))'
                   ') & '
                   '(!(x & y) -> False)')
    f = g.add_expr('x && !y')
    ep = preimage(t, f, rename, qvars, g)
    p = g.quantify(ep, {'zp'}, forall=True)
    assert p == -1
    f = g.add_expr('(x & !y) | (!x & y)')
    ep = preimage(t, f, rename, qvars, g)
    p = g.quantify(ep, {'zp'}, forall=True)
    assert p == g.add_expr('x & y')