spot/doc/org/genltl.org

genltl

#+EMAIL spot@lrde.epita.fr

This tool generates LTL formulas according to scalable patterns. These pattern are usually taken from the literature (see the 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.

      --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)))
      --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)))
      --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)
      --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)
      --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)))

An example is probably all it takes to explain how this tool works:

genltl --and-gf=1..5 --u-left=1..5

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

genltl supports the common option for output of LTL formulas, so you may output these pattern for various tools.

Note that for the --lbt output, each formula is relabeled using p0, p1, … before it is output, when the pattern (like --ccj-alpha) use different names.