1# Formulas from Gasier et al., "Rabinizer: Small deterministic
2# automata for LTL(F,G)" (ATVA'12)
3G(a | Fb)
4FGa | FGb | GFc
5F(a | b)
6GF(a | b)
7G(a | Fa)
8G(a | b | c)
9G(a | F(b | c))
10Fa | Gb
11G(a | F(b & c))
12FGa | GFb
13GF(a | b) & GF(b | c)
14
15FF(a & G!a) | (GG!a & Fa)
16GFa & FGb
17(GFa & FGb) | (FG!a & GF!b)
18FGa & GFa
19G(Fa & Fb)
20Fa & F!a
21G(b | GFa) & G(c | GF!a) | Gb | Gc
22G(b | FGa) & G(c | FG!a) | Gb | Gc
23F(b & FGa) | F(c & FG!a) & Fb & Fc
24F(b & GFa) | F(c & GF!a) & Fb & Fc
25
26GFa -> GFb
27(GFa -> GFb) & (GFc -> GFd)
28
29GF(Fa | GFb | FG(a | b))
30FG(Fa | GFb | FG(a | b))
31FG(Fa | GFb | FG(a | b) | FGb)
32
33# formulas from DBA minimizer
34XXa
35GF(a -> XXXb)
36F(p & XF(q & XF(r & XFs)))
37F(q & X(p U r))
38F(p & X(q & XFr))
39p U (q & X(r U s))
40G(a -> Fb) & G(c -> Fd)
41GFa & GFb
42GFa | GFb | GFc
43GFa
44a U b U c U d
45G(a -> Fb) & Gc
46(Ga -> Fb) & (G!a -> F!b)
47p U (q & X(r & F(s & XF(u & XF(v & XFw)))))
48G(a -> Fb) & G(b -> Fc)
49G(a -> Fb) & G(!a -> F!b)
50GFp && GFq && GF r && GF u
51GF(a <-> XXXb)
52G(p -> q U r)
53GF(a <-> XXb)
54G!c & G(a -> Fb) & G(b -> Fc)
55G(a -> XXXb)
56G(a -> Fb)
57G(a U b U !a U !b)
58(p U q U r) || (q U r U p) || (r U p U q)
59
60# Some random formulas that are determinizable with tba-det
61X((a M F((!c & !b) | (c & b))) W (G!c U b))
62X(((a & b) R (!a U !c)) R b)
63XXG(Fa U Xb)
64(!a M !b) W F!c
65(b & Fa & GFc) R a
66(a R (b W a)) W G(!a M (c | b))
67(Fa W b) R (Fc | !a)
68X(G(!a M !b) | G(a | G!a))
69Fa W Gb
70Ga | GFb
71a M G(F!b | X!a)
72G!a R XFb
73XF(!a | GFb)
74G(F!a U !a) U Xa
75(a | G(a M !b)) W Fc
76Fa W Xb
77X(a R ((!b & F!c) M X!a))
78XG!a R Fb
79GFc | (a & Fb)
80X(a R (Fb R F!b))
81G(Xa M Fa)
82X(Gb | GFa)
83X(Gc | XG((b & Ga) | (!b & F!a)))
84Ga R Fb
85G(a U (b | X((!c & !a) | (a & c))))
86XG((G!a & F!b) | (Fa & (a | Gb)))
87(a U X!a) | XG(!b & XFc)
88X(G!a | GFa)
89G(G!a | F!c | G!b)
90
91# Some random formulas that should only be determinizable via dstar2tgba
92# Generated with
93# randltl -n -1 a b c |
94# ltlfilt --remove-wm -r -u --size-min=3 --size-max=15 --syntactic-recurrence |
95# ltlfilt -v --obligation | ltl2tgba -F - -x tba-det -D --stats='%d,%f' |
96# grep 0, | head -n 30
97
98X(Fc W b) R Fa
99!b & ((Fa U b) W Xc)
100G(F!c | (Fb U a))
101(c R (b R Fa)) W XGb
102X((Fb & XFa) R XFc)
103(Ga R (F!c U b)) W b
104X(!b | G(b & !a)) R F(c & Fa)
105G(Fc | Ga | XXF!b)
106G(F(!a & Fa) U (b U Xc))
107G(F!c U X(Xb & F!b))
108G(XXFa U (b | a | Fc))
109G(c | F!a | (b U Xb))
110G(a U X(a | (F!b U Xc)))
111XF!a R F(b | (!a & F!c))
112(c & Xc) R ((!b | XFc) U a)
113G(Gb | (b & c) | F(!a & XXa))
114G(X(Fc & Xa) M Fb)
115X(!c & Fc) R (c M Fa)
116G(Ga | X(Fc U (b | X!b)))
117G(XXFb U (c | (!c & F!a)))
118((Fc U b) R Fa) W X!a
119G(a | X(a R (GFb | (Fc U a))))
120(F!c R F!b) W G!a
121(Fb & !b) R (!a R XFc)
122F(Fb & c) W Xa
123G(G!c | ((Fb U a) U c))
124(Fa & XXb) R Fc
125Gc R (F!a & (b U a))
126(c R Fa) U X!b
127GF(b & XXXFc)
128
129# Extra ones
130G(F(a & F(b & Fc)))
131(GFa & GFb) | (GFc & GFd)
132