# -*- coding: utf-8 -*- #+TITLE: =genltl= #+DESCRIPTION: Spot command-line tool that generates LTL formulas from known patterns #+INCLUDE: setup.org #+HTML_LINK_UP: tools.html #+PROPERTY: header-args:sh :results verbatim :exports both This tool outputs LTL formulas that either comes from named lists of formulas, or from scalable patterns. These patterns are usually taken from the literature (see the [[./man/genltl.1.html][=genltl=]](1) man page for references). Sometimes the same pattern is given different names in different papers, so we alias different option names to the same pattern. #+BEGIN_SRC sh :exports results genltl --help | sed -n '/Pattern selection:/,/^$/p' | sed '1d;$d' #+END_SRC #+RESULTS: #+begin_example --and-f=RANGE, --gh-e=RANGE F(p1)&F(p2)&...&F(pn) --and-fg=RANGE FG(p1)&FG(p2)&...&FG(pn) --and-gf=RANGE, --ccj-phi=RANGE, --gh-c2=RANGE GF(p1)&GF(p2)&...&GF(pn) --ccj-alpha=RANGE F(p1&F(p2&F(p3&...F(pn)))) & F(q1&F(q2&F(q3&...F(qn)))) --ccj-beta=RANGE F(p&X(p&X(p&...X(p)))) & F(q&X(q&X(q&...X(q)))) --ccj-beta-prime=RANGE F(p&(Xp)&(XXp)&...(X...X(p))) & F(q&(Xq)&(XXq)&...(X...X(q))) --dac-patterns[=RANGE], --spec-patterns[=RANGE] Dwyer et al. [FMSP'98] Spec. Patterns for LTL (range should be included in 1..55) --eh-patterns[=RANGE] Etessami and Holzmann [Concur'00] patterns (range should be included in 1..12) --fxg-or=RANGE F(p0 | XG(p1 | XG(p2 | ... XG(pn)))) --gf-equiv=RANGE (GFa1 & GFa2 & ... & GFan) <-> GFz --gf-equiv-xn=RANGE GF(a <-> X^n(a)) --gf-implies=RANGE (GFa1 & GFa2 & ... & GFan) -> GFz --gf-implies-xn=RANGE GF(a -> X^n(a)) --gh-q=RANGE (F(p1)|G(p2))&(F(p2)|G(p3))&...&(F(pn)|G(p{n+1})) --gh-r=RANGE (GF(p1)|FG(p2))&(GF(p2)|FG(p3))&... &(GF(pn)|FG(p{n+1})) --go-theta=RANGE !((GF(p1)&GF(p2)&...&GF(pn)) -> G(q->F(r))) --gxf-and=RANGE G(p0 & XF(p1 & XF(p2 & ... XF(pn)))) --hkrss-patterns[=RANGE], --liberouter-patterns[=RANGE] Holeček et al. patterns from the Liberouter project (range should be included in 1..55) --kr-n=RANGE linear formula with doubly exponential DBA --kr-nlogn=RANGE quasilinear formula with doubly exponential DBA --kv-psi=RANGE, --kr-n2=RANGE quadratic formula with doubly exponential DBA --ms-example=RANGE[,RANGE] GF(a1&X(a2&X(a3&...Xan)))&F(b1&F(b2&F(b3&...&Xbm))) --ms-phi-h=RANGE FG(a|b)|FG(!a|Xb)|FG(a|XXb)|FG(!a|XXXb)|... --ms-phi-r=RANGE (FGa{n}&GFb{n})|((FGa{n-1}|GFb{n-1})&(...)) --ms-phi-s=RANGE (FGa{n}|GFb{n})&((FGa{n-1}&GFb{n-1})|(...)) --or-fg=RANGE, --ccj-xi=RANGE FG(p1)|FG(p2)|...|FG(pn) --or-g=RANGE, --gh-s=RANGE G(p1)|G(p2)|...|G(pn) --or-gf=RANGE, --gh-c1=RANGE GF(p1)|GF(p2)|...|GF(pn) --p-patterns[=RANGE], --beem-patterns[=RANGE], --p[=RANGE] Pelánek [Spin'07] patterns from BEEM (range should be included in 1..20) --r-left=RANGE (((p1 R p2) R p3) ... R pn) --r-right=RANGE (p1 R (p2 R (... R pn))) --rv-counter=RANGE n-bit counter --rv-counter-carry=RANGE n-bit counter w/ carry --rv-counter-carry-linear=RANGE n-bit counter w/ carry (linear size) --rv-counter-linear=RANGE n-bit counter (linear size) --sb-patterns[=RANGE] Somenzi and Bloem [CAV'00] patterns (range should be included in 1..27) --sejk-f=RANGE[,RANGE] f(0,j)=(GFa0 U X^j(b)), f(i,j)=(GFai U G(f(i-1,j))) --sejk-j=RANGE (GFa1&...&GFan) -> (GFb1&...&GFbn) --sejk-k=RANGE (GFa1|FGb1)&...&(GFan|FGbn) --sejk-patterns[=RANGE] φ₁,φ₂,φ₃ from Sikert et al's [CAV'16] paper (range should be included in 1..3) --tv-f1=RANGE G(p -> (q | Xq | ... | XX...Xq) --tv-f2=RANGE G(p -> (q | X(q | X(... | Xq))) --tv-g1=RANGE G(p -> (q & Xq & ... & XX...Xq) --tv-g2=RANGE G(p -> (q & X(q & X(... & Xq))) --tv-uu=RANGE G(p1 -> (p1 U (p2 & (p2 U (p3 & (p3 U ...)))))) --u-left=RANGE, --gh-u=RANGE (((p1 U p2) U p3) ... U pn) --u-right=RANGE, --gh-u2=RANGE, --go-phi=RANGE (p1 U (p2 U (... U pn))) #+end_example An example is probably all it takes to understand how this tool works: #+BEGIN_SRC sh genltl --and-gf=1..5 --u-left=1..5 #+END_SRC #+RESULTS: #+begin_example GFp1 GFp1 & GFp2 GFp1 & GFp2 & GFp3 GFp1 & GFp2 & GFp3 & GFp4 GFp1 & GFp2 & GFp3 & GFp4 & GFp5 p1 p1 U p2 (p1 U p2) U p3 ((p1 U p2) U p3) U p4 (((p1 U p2) U p3) U p4) U p5 #+end_example =genltl= supports the [[file:ioltl.org][common option for output of LTL formulas]], so you may output these pattern for various tools. For instance here is the same formulas, but formatted in a way that is suitable for being included in a LaTeX table. #+BEGIN_SRC sh genltl --and-gf=1..5 --u-left=1..5 --latex --format='%F & %L & $%f$ \\' #+END_SRC #+RESULTS: #+begin_example and-gf & 1 & $\G \F p_{1}$ \\ and-gf & 2 & $\G \F p_{1} \land \G \F p_{2}$ \\ and-gf & 3 & $\G \F p_{1} \land \G \F p_{2} \land \G \F p_{3}$ \\ and-gf & 4 & $\G \F p_{1} \land \G \F p_{2} \land \G \F p_{3} \land \G \F p_{4}$ \\ and-gf & 5 & $\G \F p_{1} \land \G \F p_{2} \land \G \F p_{3} \land \G \F p_{4} \land \G \F p_{5}$ \\ u-left & 1 & $p_{1}$ \\ u-left & 2 & $p_{1} \U p_{2}$ \\ u-left & 3 & $(p_{1} \U p_{2}) \U p_{3}$ \\ u-left & 4 & $((p_{1} \U p_{2}) \U p_{3}) \U p_{4}$ \\ u-left & 5 & $(((p_{1} \U p_{2}) \U p_{3}) \U p_{4}) \U p_{5}$ \\ #+end_example Note that for the =--lbt= syntax, each formula is relabeled using =p0=, =p1=, ... before it is output, when the pattern (like =--ccj-alpha=) use different names. Compare: #+BEGIN_SRC sh genltl --ccj-alpha=3 #+END_SRC #+RESULTS: : F(p1 & F(p2 & Fp3)) & F(q1 & F(q2 & Fq3)) with #+BEGIN_SRC sh genltl --ccj-alpha=3 --lbt #+END_SRC #+RESULTS: : & F & p0 F & p1 F p2 F & p3 F & p4 F p5 This is because most tools using =lbt='s syntax require atomic propositions to have the form =pNN=. Five options provide lists of unrelated LTL formulas, taken from the literature (see the [[./man/genltl.1.html][=genltl=]](1) man page for references): =--dac-patterns=, =--eh-patterns=, =--hkrss-patterns=, =--p-patterns=, and =--sb-patterns=. With these options, the range is used to select a subset of the list of formulas. Without range, all formulas are used. Here is the complete list: #+BEGIN_SRC sh genltl --dac --eh --hkrss --p --sb --format='%F=%L,%f' #+END_SRC #+RESULTS: #+begin_example dac-patterns=1,G!p0 dac-patterns=2,Fp0 -> (!p1 U p0) dac-patterns=3,G(p0 -> G!p1) dac-patterns=4,G((p0 & !p1 & Fp1) -> (!p2 U p1)) dac-patterns=5,G((p0 & !p1) -> (!p2 W p1)) dac-patterns=6,Fp0 dac-patterns=7,!p0 W (!p0 & p1) dac-patterns=8,G!p0 | F(p0 & Fp1) dac-patterns=9,G((p0 & !p1) -> (!p1 W (!p1 & p2))) dac-patterns=10,G((p0 & !p1) -> (!p1 U (!p1 & p2))) dac-patterns=11,!p0 W (p0 W (!p0 W (p0 W G!p0))) dac-patterns=12,Fp0 -> ((!p0 & !p1) U (p0 | ((!p0 & p1) U (p0 | ((!p0 & !p1) U (p0 | ((!p0 & p1) U (p0 | (!p1 U p0))))))))) dac-patterns=13,Fp0 -> (!p0 U (p0 & (!p1 W (p1 W (!p1 W (p1 W G!p1)))))) dac-patterns=14,G((p0 & Fp1) -> ((!p1 & !p2) U (p1 | ((!p1 & p2) U (p1 | ((!p1 & !p2) U (p1 | ((!p1 & p2) U (p1 | (!p2 U p1)))))))))) dac-patterns=15,G(p0 -> ((!p1 & !p2) U (p2 | ((p1 & !p2) U (p2 | ((!p1 & !p2) U (p2 | ((p1 & !p2) U (p2 | (!p1 W p2) | Gp1))))))))) dac-patterns=16,Gp0 dac-patterns=17,Fp0 -> (p1 U p0) dac-patterns=18,G(p0 -> Gp1) dac-patterns=19,G((p0 & !p1 & Fp1) -> (p2 U p1)) dac-patterns=20,G((p0 & !p1) -> (p2 W p1)) dac-patterns=21,!p0 W p1 dac-patterns=22,Fp0 -> (!p1 U (p0 | p2)) dac-patterns=23,G!p0 | F(p0 & (!p1 W p2)) dac-patterns=24,G((p0 & !p1 & Fp1) -> (!p2 U (p1 | p3))) dac-patterns=25,G((p0 & !p1) -> (!p2 W (p1 | p3))) dac-patterns=26,G(p0 -> Fp1) dac-patterns=27,Fp0 -> ((p1 -> (!p0 U (!p0 & p2))) U p0) dac-patterns=28,G(p0 -> G(p1 -> Fp2)) dac-patterns=29,G((p0 & !p1 & Fp1) -> ((p2 -> (!p1 U (!p1 & p3))) U p1)) dac-patterns=30,G((p0 & !p1) -> ((p2 -> (!p1 U (!p1 & p3))) W p1)) dac-patterns=31,Fp0 -> (!p0 U (!p0 & p1 & X(!p0 U p2))) dac-patterns=32,Fp0 -> (!p1 U (p0 | (!p1 & p2 & X(!p1 U p3)))) dac-patterns=33,G!p0 | (!p0 U ((p0 & Fp1) -> (!p1 U (!p1 & p2 & X(!p1 U p3))))) dac-patterns=34,G((p0 & Fp1) -> (!p2 U (p1 | (!p2 & p3 & X(!p2 U p4))))) dac-patterns=35,G(p0 -> (Fp1 -> (!p1 U (p2 | (!p1 & p3 & X(!p1 U p4)))))) dac-patterns=36,F(p0 & XFp1) -> (!p0 U p2) dac-patterns=37,Fp0 -> (!(!p0 & p1 & X(!p0 U (!p0 & p2))) U (p0 | p3)) dac-patterns=38,G!p0 | (!p0 U (p0 & (F(p1 & XFp2) -> (!p1 U p3)))) dac-patterns=39,G((p0 & Fp1) -> (!(!p1 & p2 & X(!p1 U (!p1 & p3))) U (p1 | p4))) dac-patterns=40,G(p0 -> ((!(!p1 & p2 & X(!p1 U (!p1 & p3))) U (p1 | p4)) | G!(p2 & XFp3))) dac-patterns=41,G((p0 & XFp1) -> XF(p1 & Fp2)) dac-patterns=42,Fp0 -> (((p1 & X(!p0 U p2)) -> X(!p0 U (p2 & Fp3))) U p0) dac-patterns=43,G(p0 -> G((p1 & XFp2) -> X(!p2 U (p2 & Fp3)))) dac-patterns=44,G((p0 & Fp1) -> (((p2 & X(!p1 U p3)) -> X(!p1 U (p3 & Fp4))) U p1)) dac-patterns=45,G(p0 -> (((p1 & X(!p2 U p3)) -> X(!p2 U (p3 & Fp4))) U (p2 | G((p1 & X(!p2 U p3)) -> X(!p2 U (p3 & Fp4)))))) dac-patterns=46,G(p0 -> F(p1 & XFp2)) dac-patterns=47,Fp0 -> ((p1 -> (!p0 U (!p0 & p2 & X(!p0 U p3)))) U p0) dac-patterns=48,G(p0 -> G(p1 -> (p2 & XFp3))) dac-patterns=49,G((p0 & Fp1) -> ((p2 -> (!p1 U (!p1 & p3 & X(!p1 U p4)))) U p1)) dac-patterns=50,G(p0 -> ((p1 -> (!p2 U (!p2 & p3 & X(!p2 U p4)))) U (p2 | G(p1 -> (p3 & XFp4))))) dac-patterns=51,G(p0 -> F(p1 & !p2 & X(!p2 U p3))) dac-patterns=52,Fp0 -> ((p1 -> (!p0 U (!p0 & p2 & !p3 & X((!p0 & !p3) U p4)))) U p0) dac-patterns=53,G(p0 -> G(p1 -> (p2 & !p3 & X(!p3 U p4)))) dac-patterns=54,G((p0 & Fp1) -> ((p2 -> (!p1 U (!p1 & p3 & !p4 & X((!p1 & !p4) U p5)))) U p1)) dac-patterns=55,G(p0 -> ((p1 -> (!p2 U (!p2 & p3 & !p4 & X((!p2 & !p4) U p5)))) U (p2 | G(p1 -> (p3 & !p4 & X(!p4 U p5)))))) eh-patterns=1,p0 U (p1 & Gp2) eh-patterns=2,p0 U (p1 & X(p2 U p3)) eh-patterns=3,p0 U (p1 & X(p2 & F(p3 & XF(p4 & XF(p5 & XFp6))))) eh-patterns=4,F(p0 & XGp1) eh-patterns=5,F(p0 & X(p1 & XFp2)) eh-patterns=6,F(p0 & X(p1 U p2)) eh-patterns=7,FGp0 | GFp1 eh-patterns=8,G(p0 -> (p1 U p2)) eh-patterns=9,G(p0 & XF(p1 & XF(p2 & XFp3))) eh-patterns=10,GFp0 & GFp1 & GFp2 & GFp3 & GFp4 eh-patterns=11,(p0 U (p1 U p2)) | (p1 U (p2 U p0)) | (p2 U (p0 U p1)) eh-patterns=12,G(p0 -> (p1 U (Gp2 | Gp3))) hkrss-patterns=1,G(Fp0 & F!p0) hkrss-patterns=2,GFp0 & GF!p0 hkrss-patterns=3,GF(!(p1 <-> Xp1) | !(p0 <-> Xp0)) hkrss-patterns=4,GF(!(p1 <-> Xp1) | !(p0 <-> Xp0) | !(p2 <-> Xp2) | !(p3 <-> Xp3)) hkrss-patterns=5,G!p0 hkrss-patterns=6,G((p0 -> F!p0) & (!p0 -> Fp0)) hkrss-patterns=7,G(p0 -> F(p0 & p1)) hkrss-patterns=8,G(p0 -> F((!p0 & p1 & p2 & p3) -> Fp4)) hkrss-patterns=9,G(p0 -> F!p1) hkrss-patterns=10,G(p0 -> Fp1) hkrss-patterns=11,G(p0 -> F(p1 -> Fp2)) hkrss-patterns=12,G(p0 -> F((p1 & p2) -> Fp3)) hkrss-patterns=13,G((p0 -> Fp1) & (p2 -> Fp3) & (p4 -> Fp5) & (p6 -> Fp7)) hkrss-patterns=14,G(!p0 & !p1) hkrss-patterns=15,G!(p0 & p1) hkrss-patterns=16,G(p0 -> p1) hkrss-patterns=17,G((p0 -> !p1) & (p1 -> !p0)) hkrss-patterns=18,G(!p0 -> (p1 <-> !p2)) hkrss-patterns=19,G((!p0 & (p1 | p2 | p3)) -> p4) hkrss-patterns=20,G((p0 & p1) -> (p2 | !(p3 & p4))) hkrss-patterns=21,G((!p0 & p1 & !p2 & !p3 & !p4) -> F(!p5 & !p6 & !p7 & !p8)) hkrss-patterns=22,G((p0 & p1 & !p2 & !p3 & !p4) -> F(p5 & !p6 & !p7 & !p8)) hkrss-patterns=23,G(!p0 -> !(p1 & p2 & p3 & p4 & p5)) hkrss-patterns=24,G(!p0 -> ((p1 & p2 & p3 & p4) -> !p5)) hkrss-patterns=25,G((p0 & p1) -> (p2 | p3 | !(p4 & p5))) hkrss-patterns=26,G((!p0 & (p1 | p2 | p3 | p4)) -> (!p5 <-> p6)) hkrss-patterns=27,G((p0 & p1) -> (p2 | p3 | p4 | !(p5 & p6))) hkrss-patterns=28,G((p0 & p1) -> (p2 | p3 | p4 | p5 | !(p6 & p7))) hkrss-patterns=29,G((p0 & p1 & !p2 & Xp2) -> X(p3 | X(!p1 | p3))) hkrss-patterns=30,G((p0 & p1 & !p2 & Xp2) -> X(X!p1 | (p2 U (!p2 U (p2 U (!p1 | p3)))))) hkrss-patterns=31,G(p0 & p1 & !p2 & Xp2) -> X(X!p1 | (p2 U (!p2 U (p2 U (!p1 | p3))))) hkrss-patterns=32,G(p0 -> (p1 U (!p1 U (!p2 | p3)))) hkrss-patterns=33,G(p0 -> (p1 U (!p1 U (p2 | p3)))) hkrss-patterns=34,G((!p0 & p1) -> Xp2) hkrss-patterns=35,G(p0 -> X(p0 | p1)) hkrss-patterns=36,G((!(p1 <-> Xp1) | !(p0 <-> Xp0) | !(p2 <-> Xp2) | !(p3 <-> Xp3)) -> (X!p4 & X(!(!(p1 <-> Xp1) | !(p0 <-> Xp0) | !(p2 <-> Xp2) | !(p3 <-> Xp3)) U p4))) hkrss-patterns=37,G((p0 & !p1 & Xp1 & Xp0) -> (p2 -> Xp3)) hkrss-patterns=38,G(p0 -> X(!p0 U p1)) hkrss-patterns=39,G((!p0 & Xp0) -> X((p0 U p1) | Gp0)) hkrss-patterns=40,G((!p0 & Xp0) -> X(p0 U (p0 & !p1 & X(p0 & p1)))) hkrss-patterns=41,G((!p0 & Xp0) -> X(p0 U (p0 & !p1 & X(p0 & p1 & (p0 U (p0 & !p1 & X(p0 & p1))))))) hkrss-patterns=42,G((p0 & X!p0) -> X(!p0 U (!p0 & !p1 & X(!p0 & p1 & (!p0 U (!p0 & !p1 & X(!p0 & p1))))))) hkrss-patterns=43,G((p0 & X!p0) -> X(!p0 U (!p0 & !p1 & X(!p0 & p1 & (!p0 U (!p0 & !p1 & X(!p0 & p1 & (!p0 U (!p0 & !p1 & X(!p0 & p1)))))))))) hkrss-patterns=44,G((!p0 & Xp0) -> X(!(!p0 & Xp0) U (!p1 & Xp1))) hkrss-patterns=45,G(!p0 | X(!p0 | X(!p0 | X(!p0 | X(!p0 | X(!p0 | X(!p0 | X(!p0 | X(!p0 | X(!p0 | X(!p0 | X!p0))))))))))) hkrss-patterns=46,G((Xp0 -> p0) -> (p1 <-> Xp1)) hkrss-patterns=47,G((Xp0 -> p0) -> ((p1 -> Xp1) & (!p1 -> X!p1))) hkrss-patterns=48,!p0 U G!((p1 & p2) | (p3 & p4) | (p2 & p3) | (p2 & p4) | (p1 & p4) | (p1 & p3)) hkrss-patterns=49,!p0 U p1 hkrss-patterns=50,(p0 U p1) | Gp0 hkrss-patterns=51,p0 & XG!p0 hkrss-patterns=52,XG(p0 -> (G!p1 | (!Xp1 U p2))) hkrss-patterns=53,XG((p0 & !p1) -> (G!p1 | (!p1 U p2))) hkrss-patterns=54,XG((p0 & p1) -> ((p1 U p2) | Gp1)) hkrss-patterns=55,Xp0 & G((!p0 & Xp0) -> XXp0) p-patterns=1,G(p0 -> Fp1) p-patterns=2,(GFp1 & GFp0) -> GFp2 p-patterns=3,G(p0 -> (p1 & (p2 U p3))) p-patterns=4,F(p0 | p1) p-patterns=5,GF(p0 | p1) p-patterns=6,(p0 U p1) -> ((p2 U p3) | Gp2) p-patterns=7,G(p0 -> (!p1 U (p1 U (!p1 & (p2 R !p1))))) p-patterns=8,G(p0 -> (p1 R !p2)) p-patterns=9,G(!p0 -> Fp0) p-patterns=10,G(p0 -> F(p1 | p2)) p-patterns=11,!(!(p0 | p1) U p2) & G(p3 -> !(!(p0 | p1) U p2)) p-patterns=12,G!p0 -> G!p1 p-patterns=13,G(p0 -> (G!p1 | (!p2 U p1))) p-patterns=14,G(p0 -> (p1 R (p1 | !p2))) p-patterns=15,G((p0 & p1) -> (!p1 R (p0 | !p1))) p-patterns=16,G(p0 -> F(p1 & p2)) p-patterns=17,G(p0 -> (!p1 U (p1 U (p1 & p2)))) p-patterns=18,G(p0 -> (!p1 U (p1 U (!p1 U (p1 U (p1 & p2)))))) p-patterns=19,GFp0 -> GFp1 p-patterns=20,GF(p0 | p1) & GF(p1 | p2) sb-patterns=1,p0 U p1 sb-patterns=2,p0 U (p1 U p2) sb-patterns=3,!(p0 U (p1 U p2)) sb-patterns=4,GFp0 -> GFp1 sb-patterns=5,Fp0 U Gp1 sb-patterns=6,Gp0 U p1 sb-patterns=7,!(Fp0 <-> Fp1) sb-patterns=8,!(GFp0 -> GFp1) sb-patterns=9,!(GFp0 <-> GFp1) sb-patterns=10,p0 R (p0 | p1) sb-patterns=11,(Xp0 U Xp1) | !X(p0 U p1) sb-patterns=12,(Xp0 U p1) | !X(p0 U (p0 & p1)) sb-patterns=13,G(p0 -> Fp1) & ((Xp0 U p1) | !X(p0 U (p0 & p1))) sb-patterns=14,G(p0 -> Fp1) & ((Xp0 U Xp1) | !X(p0 U p1)) sb-patterns=15,G(p0 -> Fp1) sb-patterns=16,!G(p0 -> X(p1 R p2)) sb-patterns=17,!(FGp0 | FGp1) sb-patterns=18,G(Fp0 & Fp1) sb-patterns=19,Fp0 & F!p0 sb-patterns=20,(p0 & Xp1) R X(((p2 U p3) R p0) U (p2 R p0)) sb-patterns=21,Gp2 | (G(p0 | GFp1) & G(p2 | GF!p1)) | Gp0 sb-patterns=22,Gp0 | Gp2 | (G(p0 | FGp1) & G(p2 | FG!p1)) sb-patterns=23,!(Gp2 | (G(p0 | GFp1) & G(p2 | GF!p1)) | Gp0) sb-patterns=24,!(Gp0 | Gp2 | (G(p0 | FGp1) & G(p2 | FG!p1))) sb-patterns=25,G(p0 | XGp1) & G(p2 | XG!p1) sb-patterns=26,G(p0 | (Xp1 & X!p1)) sb-patterns=27,p0 | (p1 U p0) #+end_example Note that ~--sb-patterns=2 --sb-patterns=4 --sb-patterns=21..22~ also have their complement formulas listed as ~--sb-patterns=3 --sb-patterns=8 --sb-patterns=23..24~. So if you build the set of formulas output by =genltl --sb-patterns= plus their negations, it will contain only 46 formulas, not 54. #+BEGIN_SRC sh genltl --sb | ltlfilt --uniq --count genltl --sb --pos --neg | ltlfilt --uniq --count #+END_SRC #+RESULTS: : 27 : 46 # LocalWords: genltl num toc LTL scalable SRC sed gh pn fg FG gf qn # LocalWords: ccj Xp XXp Xq XXq rv GFp lbt utf SETUPFILE html dac # LocalWords: Dwyer et al FMSP Etessami Holzmann sb Somenzi Bloem # LocalWords: CAV LaTeX Fq Fp pNN Gp XFp XF XGp FGp XG ltlfilt uniq # LocalWords: args fxg GFa GFan GFz xn gxf hkrss liberouter Holeček # LocalWords: kr DBA nlogn quasilinear kv Xb XXb XXXb FGa GFb beem # LocalWords: Pelánek sejk GFai GFbn FGb FGbn Sikert al's tv uu pos