7dfeda8e77
This feature is in Org 9, which is already required. * doc/org/autcross.org, doc/org/autfilt.org, doc/org/compile.org, doc/org/concepts.org, doc/org/csv.org, doc/org/dstar2tgba.org, doc/org/genaut.org, doc/org/genltl.org, doc/org/hierarchy.org, doc/org/hoa.org, doc/org/ioltl.org, doc/org/ltl2tgba.org, doc/org/ltl2tgta.org, doc/org/ltlcross.org, doc/org/ltldo.org, doc/org/ltlfilt.org, doc/org/ltlgrind.org, doc/org/ltlsynt.org, doc/org/oaut.org, doc/org/randaut.org, doc/org/randltl.org, doc/org/satmin.org, doc/org/setup.org, doc/org/tools.org, doc/org/tut01.org, doc/org/tut02.org, doc/org/tut03.org, doc/org/tut04.org, doc/org/tut10.org, doc/org/tut11.org, doc/org/tut12.org, doc/org/tut20.org, doc/org/tut21.org, doc/org/tut22.org, doc/org/tut23.org, doc/org/tut24.org, doc/org/tut30.org, doc/org/tut31.org, doc/org/tut50.org, doc/org/upgrade2.org: Simplify SRC block setups for sh, python and C++. Also fix a few typos and examples along the way.
358 lines
16 KiB
Org Mode
358 lines
16 KiB
Org Mode
# -*- coding: utf-8 -*-
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#+TITLE: =genltl=
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#+DESCRIPTION: Spot command-line tool that generates LTL formulas from known patterns
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#+INCLUDE: setup.org
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#+HTML_LINK_UP: tools.html
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#+PROPERTY: header-args:sh :results verbatim :exports both
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This tool outputs LTL formulas that either comes from named lists of
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formulas, or from scalable patterns.
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These patterns are usually taken from the literature (see the
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[[./man/genltl.1.html][=genltl=]](1) man page for references). Sometimes the same pattern is
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given different names in different papers, so we alias different
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option names to the same pattern.
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#+BEGIN_SRC sh :exports results
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genltl --help | sed -n '/Pattern selection:/,/^$/p' | sed '1d;$d'
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#+END_SRC
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#+RESULTS:
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#+begin_example
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--and-f=RANGE, --gh-e=RANGE
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F(p1)&F(p2)&...&F(pn)
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--and-fg=RANGE FG(p1)&FG(p2)&...&FG(pn)
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--and-gf=RANGE, --ccj-phi=RANGE, --gh-c2=RANGE
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GF(p1)&GF(p2)&...&GF(pn)
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--ccj-alpha=RANGE F(p1&F(p2&F(p3&...F(pn)))) &
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F(q1&F(q2&F(q3&...F(qn))))
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--ccj-beta=RANGE F(p&X(p&X(p&...X(p)))) & F(q&X(q&X(q&...X(q))))
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--ccj-beta-prime=RANGE F(p&(Xp)&(XXp)&...(X...X(p))) &
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F(q&(Xq)&(XXq)&...(X...X(q)))
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--dac-patterns[=RANGE], --spec-patterns[=RANGE]
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Dwyer et al. [FMSP'98] Spec. Patterns for LTL
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(range should be included in 1..55)
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--eh-patterns[=RANGE] Etessami and Holzmann [Concur'00] patterns (range
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should be included in 1..12)
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--fxg-or=RANGE F(p0 | XG(p1 | XG(p2 | ... XG(pn))))
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--gf-equiv=RANGE (GFa1 & GFa2 & ... & GFan) <-> GFz
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--gf-equiv-xn=RANGE GF(a <-> X^n(a))
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--gf-implies=RANGE (GFa1 & GFa2 & ... & GFan) -> GFz
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--gf-implies-xn=RANGE GF(a -> X^n(a))
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--gh-q=RANGE (F(p1)|G(p2))&(F(p2)|G(p3))&...&(F(pn)|G(p{n+1}))
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--gh-r=RANGE (GF(p1)|FG(p2))&(GF(p2)|FG(p3))&...
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&(GF(pn)|FG(p{n+1}))
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--go-theta=RANGE !((GF(p1)&GF(p2)&...&GF(pn)) -> G(q->F(r)))
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--gxf-and=RANGE G(p0 & XF(p1 & XF(p2 & ... XF(pn))))
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--hkrss-patterns[=RANGE], --liberouter-patterns[=RANGE]
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Holeček et al. patterns from the Liberouter
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project (range should be included in 1..55)
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--kr-n=RANGE linear formula with doubly exponential DBA
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--kr-nlogn=RANGE quasilinear formula with doubly exponential DBA
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--kv-psi=RANGE, --kr-n2=RANGE
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quadratic formula with doubly exponential DBA
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--ms-example=RANGE[,RANGE]
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GF(a1&X(a2&X(a3&...Xan)))&F(b1&F(b2&F(b3&...&Xbm)))
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--ms-phi-h=RANGE FG(a|b)|FG(!a|Xb)|FG(a|XXb)|FG(!a|XXXb)|...
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--ms-phi-r=RANGE (FGa{n}&GFb{n})|((FGa{n-1}|GFb{n-1})&(...))
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--ms-phi-s=RANGE (FGa{n}|GFb{n})&((FGa{n-1}&GFb{n-1})|(...))
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--or-fg=RANGE, --ccj-xi=RANGE
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FG(p1)|FG(p2)|...|FG(pn)
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--or-g=RANGE, --gh-s=RANGE G(p1)|G(p2)|...|G(pn)
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--or-gf=RANGE, --gh-c1=RANGE
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GF(p1)|GF(p2)|...|GF(pn)
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--p-patterns[=RANGE], --beem-patterns[=RANGE], --p[=RANGE]
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Pelánek [Spin'07] patterns from BEEM (range
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should be included in 1..20)
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--r-left=RANGE (((p1 R p2) R p3) ... R pn)
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--r-right=RANGE (p1 R (p2 R (... R pn)))
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--rv-counter=RANGE n-bit counter
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--rv-counter-carry=RANGE n-bit counter w/ carry
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--rv-counter-carry-linear=RANGE
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n-bit counter w/ carry (linear size)
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--rv-counter-linear=RANGE n-bit counter (linear size)
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--sb-patterns[=RANGE] Somenzi and Bloem [CAV'00] patterns (range should
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be included in 1..27)
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--sejk-f=RANGE[,RANGE] f(0,j)=(GFa0 U X^j(b)), f(i,j)=(GFai U
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G(f(i-1,j)))
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--sejk-j=RANGE (GFa1&...&GFan) -> (GFb1&...&GFbn)
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--sejk-k=RANGE (GFa1|FGb1)&...&(GFan|FGbn)
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--sejk-patterns[=RANGE] φ₁,φ₂,φ₃ from Sikert et al's [CAV'16]
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paper (range should be included in 1..3)
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--tv-f1=RANGE G(p -> (q | Xq | ... | XX...Xq)
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--tv-f2=RANGE G(p -> (q | X(q | X(... | Xq)))
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--tv-g1=RANGE G(p -> (q & Xq & ... & XX...Xq)
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--tv-g2=RANGE G(p -> (q & X(q & X(... & Xq)))
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--tv-uu=RANGE G(p1 -> (p1 U (p2 & (p2 U (p3 & (p3 U ...))))))
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--u-left=RANGE, --gh-u=RANGE
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(((p1 U p2) U p3) ... U pn)
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--u-right=RANGE, --gh-u2=RANGE, --go-phi=RANGE
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(p1 U (p2 U (... U pn)))
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#+end_example
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An example is probably all it takes to understand how this tool works:
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#+BEGIN_SRC sh
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genltl --and-gf=1..5 --u-left=1..5
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#+END_SRC
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#+RESULTS:
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#+begin_example
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GFp1
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GFp1 & GFp2
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GFp1 & GFp2 & GFp3
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GFp1 & GFp2 & GFp3 & GFp4
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GFp1 & GFp2 & GFp3 & GFp4 & GFp5
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p1
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p1 U p2
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(p1 U p2) U p3
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((p1 U p2) U p3) U p4
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(((p1 U p2) U p3) U p4) U p5
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#+end_example
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=genltl= supports the [[file:ioltl.org][common option for output of LTL formulas]], so you
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may output these pattern for various tools.
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For instance here is the same formulas, but formatted in a way that is
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suitable for being included in a LaTeX table.
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#+BEGIN_SRC sh
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genltl --and-gf=1..5 --u-left=1..5 --latex --format='%F & %L & $%f$ \\'
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#+END_SRC
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#+RESULTS:
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#+begin_example
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and-gf & 1 & $\G \F p_{1}$ \\
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and-gf & 2 & $\G \F p_{1} \land \G \F p_{2}$ \\
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and-gf & 3 & $\G \F p_{1} \land \G \F p_{2} \land \G \F p_{3}$ \\
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and-gf & 4 & $\G \F p_{1} \land \G \F p_{2} \land \G \F p_{3} \land \G \F p_{4}$ \\
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and-gf & 5 & $\G \F p_{1} \land \G \F p_{2} \land \G \F p_{3} \land \G \F p_{4} \land \G \F p_{5}$ \\
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u-left & 1 & $p_{1}$ \\
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u-left & 2 & $p_{1} \U p_{2}$ \\
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u-left & 3 & $(p_{1} \U p_{2}) \U p_{3}$ \\
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u-left & 4 & $((p_{1} \U p_{2}) \U p_{3}) \U p_{4}$ \\
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u-left & 5 & $(((p_{1} \U p_{2}) \U p_{3}) \U p_{4}) \U p_{5}$ \\
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#+end_example
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Note that for the =--lbt= syntax, each formula is relabeled using
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=p0=, =p1=, ... before it is output, when the pattern (like
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=--ccj-alpha=) use different names. Compare:
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#+BEGIN_SRC sh
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genltl --ccj-alpha=3
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#+END_SRC
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#+RESULTS:
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: F(p1 & F(p2 & Fp3)) & F(q1 & F(q2 & Fq3))
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with
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#+BEGIN_SRC sh
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genltl --ccj-alpha=3 --lbt
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#+END_SRC
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#+RESULTS:
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: & F & p0 F & p1 F p2 F & p3 F & p4 F p5
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This is because most tools using =lbt='s syntax require atomic
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propositions to have the form =pNN=.
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Five options provide lists of unrelated LTL formulas, taken from the
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literature (see the [[./man/genltl.1.html][=genltl=]](1) man page for references):
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=--dac-patterns=, =--eh-patterns=, =--hkrss-patterns=, =--p-patterns=,
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and =--sb-patterns=. With these options, the range is used to select
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a subset of the list of formulas. Without range, all formulas are
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used. Here is the complete list:
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#+BEGIN_SRC sh
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genltl --dac --eh --hkrss --p --sb --format='%F=%L,%f'
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#+END_SRC
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#+RESULTS:
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#+begin_example
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dac-patterns=1,G!p0
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dac-patterns=2,Fp0 -> (!p1 U p0)
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dac-patterns=3,G(p0 -> G!p1)
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dac-patterns=4,G((p0 & !p1 & Fp1) -> (!p2 U p1))
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dac-patterns=5,G((p0 & !p1) -> (!p2 W p1))
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dac-patterns=6,Fp0
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dac-patterns=7,!p0 W (!p0 & p1)
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dac-patterns=8,G!p0 | F(p0 & Fp1)
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dac-patterns=9,G((p0 & !p1) -> (!p1 W (!p1 & p2)))
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dac-patterns=10,G((p0 & !p1) -> (!p1 U (!p1 & p2)))
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dac-patterns=11,!p0 W (p0 W (!p0 W (p0 W G!p0)))
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dac-patterns=12,Fp0 -> ((!p0 & !p1) U (p0 | ((!p0 & p1) U (p0 | ((!p0 & !p1) U (p0 | ((!p0 & p1) U (p0 | (!p1 U p0)))))))))
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dac-patterns=13,Fp0 -> (!p0 U (p0 & (!p1 W (p1 W (!p1 W (p1 W G!p1))))))
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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))))))))))
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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)))))))))
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dac-patterns=16,Gp0
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dac-patterns=17,Fp0 -> (p1 U p0)
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dac-patterns=18,G(p0 -> Gp1)
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dac-patterns=19,G((p0 & !p1 & Fp1) -> (p2 U p1))
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dac-patterns=20,G((p0 & !p1) -> (p2 W p1))
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dac-patterns=21,!p0 W p1
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dac-patterns=22,Fp0 -> (!p1 U (p0 | p2))
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dac-patterns=23,G!p0 | F(p0 & (!p1 W p2))
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dac-patterns=24,G((p0 & !p1 & Fp1) -> (!p2 U (p1 | p3)))
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dac-patterns=25,G((p0 & !p1) -> (!p2 W (p1 | p3)))
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dac-patterns=26,G(p0 -> Fp1)
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dac-patterns=27,Fp0 -> ((p1 -> (!p0 U (!p0 & p2))) U p0)
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dac-patterns=28,G(p0 -> G(p1 -> Fp2))
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dac-patterns=29,G((p0 & !p1 & Fp1) -> ((p2 -> (!p1 U (!p1 & p3))) U p1))
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dac-patterns=30,G((p0 & !p1) -> ((p2 -> (!p1 U (!p1 & p3))) W p1))
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dac-patterns=31,Fp0 -> (!p0 U (!p0 & p1 & X(!p0 U p2)))
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dac-patterns=32,Fp0 -> (!p1 U (p0 | (!p1 & p2 & X(!p1 U p3))))
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dac-patterns=33,G!p0 | (!p0 U ((p0 & Fp1) -> (!p1 U (!p1 & p2 & X(!p1 U p3)))))
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dac-patterns=34,G((p0 & Fp1) -> (!p2 U (p1 | (!p2 & p3 & X(!p2 U p4)))))
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dac-patterns=35,G(p0 -> (Fp1 -> (!p1 U (p2 | (!p1 & p3 & X(!p1 U p4))))))
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dac-patterns=36,F(p0 & XFp1) -> (!p0 U p2)
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dac-patterns=37,Fp0 -> (!(!p0 & p1 & X(!p0 U (!p0 & p2))) U (p0 | p3))
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dac-patterns=38,G!p0 | (!p0 U (p0 & (F(p1 & XFp2) -> (!p1 U p3))))
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dac-patterns=39,G((p0 & Fp1) -> (!(!p1 & p2 & X(!p1 U (!p1 & p3))) U (p1 | p4)))
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dac-patterns=40,G(p0 -> ((!(!p1 & p2 & X(!p1 U (!p1 & p3))) U (p1 | p4)) | G!(p2 & XFp3)))
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dac-patterns=41,G((p0 & XFp1) -> XF(p1 & Fp2))
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dac-patterns=42,Fp0 -> (((p1 & X(!p0 U p2)) -> X(!p0 U (p2 & Fp3))) U p0)
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dac-patterns=43,G(p0 -> G((p1 & XFp2) -> X(!p2 U (p2 & Fp3))))
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dac-patterns=44,G((p0 & Fp1) -> (((p2 & X(!p1 U p3)) -> X(!p1 U (p3 & Fp4))) U p1))
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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))))))
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dac-patterns=46,G(p0 -> F(p1 & XFp2))
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dac-patterns=47,Fp0 -> ((p1 -> (!p0 U (!p0 & p2 & X(!p0 U p3)))) U p0)
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dac-patterns=48,G(p0 -> G(p1 -> (p2 & XFp3)))
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dac-patterns=49,G((p0 & Fp1) -> ((p2 -> (!p1 U (!p1 & p3 & X(!p1 U p4)))) U p1))
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dac-patterns=50,G(p0 -> ((p1 -> (!p2 U (!p2 & p3 & X(!p2 U p4)))) U (p2 | G(p1 -> (p3 & XFp4)))))
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dac-patterns=51,G(p0 -> F(p1 & !p2 & X(!p2 U p3)))
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dac-patterns=52,Fp0 -> ((p1 -> (!p0 U (!p0 & p2 & !p3 & X((!p0 & !p3) U p4)))) U p0)
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dac-patterns=53,G(p0 -> G(p1 -> (p2 & !p3 & X(!p3 U p4))))
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dac-patterns=54,G((p0 & Fp1) -> ((p2 -> (!p1 U (!p1 & p3 & !p4 & X((!p1 & !p4) U p5)))) U p1))
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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))))))
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eh-patterns=1,p0 U (p1 & Gp2)
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eh-patterns=2,p0 U (p1 & X(p2 U p3))
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eh-patterns=3,p0 U (p1 & X(p2 & F(p3 & XF(p4 & XF(p5 & XFp6)))))
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eh-patterns=4,F(p0 & XGp1)
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eh-patterns=5,F(p0 & X(p1 & XFp2))
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eh-patterns=6,F(p0 & X(p1 U p2))
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eh-patterns=7,FGp0 | GFp1
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eh-patterns=8,G(p0 -> (p1 U p2))
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eh-patterns=9,G(p0 & XF(p1 & XF(p2 & XFp3)))
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eh-patterns=10,GFp0 & GFp1 & GFp2 & GFp3 & GFp4
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eh-patterns=11,(p0 U (p1 U p2)) | (p1 U (p2 U p0)) | (p2 U (p0 U p1))
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eh-patterns=12,G(p0 -> (p1 U (Gp2 | Gp3)))
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hkrss-patterns=1,G(Fp0 & F!p0)
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hkrss-patterns=2,GFp0 & GF!p0
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hkrss-patterns=3,GF(!(p1 <-> Xp1) | !(p0 <-> Xp0))
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hkrss-patterns=4,GF(!(p1 <-> Xp1) | !(p0 <-> Xp0) | !(p2 <-> Xp2) | !(p3 <-> Xp3))
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hkrss-patterns=5,G!p0
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hkrss-patterns=6,G((p0 -> F!p0) & (!p0 -> Fp0))
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hkrss-patterns=7,G(p0 -> F(p0 & p1))
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hkrss-patterns=8,G(p0 -> F((!p0 & p1 & p2 & p3) -> Fp4))
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hkrss-patterns=9,G(p0 -> F!p1)
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hkrss-patterns=10,G(p0 -> Fp1)
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hkrss-patterns=11,G(p0 -> F(p1 -> Fp2))
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hkrss-patterns=12,G(p0 -> F((p1 & p2) -> Fp3))
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hkrss-patterns=13,G((p0 -> Fp1) & (p2 -> Fp3) & (p4 -> Fp5) & (p6 -> Fp7))
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hkrss-patterns=14,G(!p0 & !p1)
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hkrss-patterns=15,G!(p0 & p1)
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hkrss-patterns=16,G(p0 -> p1)
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hkrss-patterns=17,G((p0 -> !p1) & (p1 -> !p0))
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hkrss-patterns=18,G(!p0 -> (p1 <-> !p2))
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hkrss-patterns=19,G((!p0 & (p1 | p2 | p3)) -> p4)
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hkrss-patterns=20,G((p0 & p1) -> (p2 | !(p3 & p4)))
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hkrss-patterns=21,G((!p0 & p1 & !p2 & !p3 & !p4) -> F(!p5 & !p6 & !p7 & !p8))
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hkrss-patterns=22,G((p0 & p1 & !p2 & !p3 & !p4) -> F(p5 & !p6 & !p7 & !p8))
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hkrss-patterns=23,G(!p0 -> !(p1 & p2 & p3 & p4 & p5))
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hkrss-patterns=24,G(!p0 -> ((p1 & p2 & p3 & p4) -> !p5))
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hkrss-patterns=25,G((p0 & p1) -> (p2 | p3 | !(p4 & p5)))
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hkrss-patterns=26,G((!p0 & (p1 | p2 | p3 | p4)) -> (!p5 <-> p6))
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hkrss-patterns=27,G((p0 & p1) -> (p2 | p3 | p4 | !(p5 & p6)))
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hkrss-patterns=28,G((p0 & p1) -> (p2 | p3 | p4 | p5 | !(p6 & p7)))
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hkrss-patterns=29,G((p0 & p1 & !p2 & Xp2) -> X(p3 | X(!p1 | p3)))
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hkrss-patterns=30,G((p0 & p1 & !p2 & Xp2) -> X(X!p1 | (p2 U (!p2 U (p2 U (!p1 | p3))))))
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hkrss-patterns=31,G(p0 & p1 & !p2 & Xp2) -> X(X!p1 | (p2 U (!p2 U (p2 U (!p1 | p3)))))
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hkrss-patterns=32,G(p0 -> (p1 U (!p1 U (!p2 | p3))))
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hkrss-patterns=33,G(p0 -> (p1 U (!p1 U (p2 | p3))))
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hkrss-patterns=34,G((!p0 & p1) -> Xp2)
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hkrss-patterns=35,G(p0 -> X(p0 | p1))
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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)))
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hkrss-patterns=37,G((p0 & !p1 & Xp1 & Xp0) -> (p2 -> Xp3))
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hkrss-patterns=38,G(p0 -> X(!p0 U p1))
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hkrss-patterns=39,G((!p0 & Xp0) -> X((p0 U p1) | Gp0))
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hkrss-patterns=40,G((!p0 & Xp0) -> X(p0 U (p0 & !p1 & X(p0 & p1))))
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hkrss-patterns=41,G((!p0 & Xp0) -> X(p0 U (p0 & !p1 & X(p0 & p1 & (p0 U (p0 & !p1 & X(p0 & p1)))))))
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hkrss-patterns=42,G((p0 & X!p0) -> X(!p0 U (!p0 & !p1 & X(!p0 & p1 & (!p0 U (!p0 & !p1 & X(!p0 & p1)))))))
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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))))))))))
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hkrss-patterns=44,G((!p0 & Xp0) -> X(!(!p0 & Xp0) U (!p1 & Xp1)))
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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)))))))))))
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hkrss-patterns=46,G((Xp0 -> p0) -> (p1 <-> Xp1))
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hkrss-patterns=47,G((Xp0 -> p0) -> ((p1 -> Xp1) & (!p1 -> X!p1)))
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hkrss-patterns=48,!p0 U G!((p1 & p2) | (p3 & p4) | (p2 & p3) | (p2 & p4) | (p1 & p4) | (p1 & p3))
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hkrss-patterns=49,!p0 U p1
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hkrss-patterns=50,(p0 U p1) | Gp0
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hkrss-patterns=51,p0 & XG!p0
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hkrss-patterns=52,XG(p0 -> (G!p1 | (!Xp1 U p2)))
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hkrss-patterns=53,XG((p0 & !p1) -> (G!p1 | (!p1 U p2)))
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hkrss-patterns=54,XG((p0 & p1) -> ((p1 U p2) | Gp1))
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hkrss-patterns=55,Xp0 & G((!p0 & Xp0) -> XXp0)
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p-patterns=1,G(p0 -> Fp1)
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p-patterns=2,(GFp1 & GFp0) -> GFp2
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p-patterns=3,G(p0 -> (p1 & (p2 U p3)))
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p-patterns=4,F(p0 | p1)
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p-patterns=5,GF(p0 | p1)
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p-patterns=6,(p0 U p1) -> ((p2 U p3) | Gp2)
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p-patterns=7,G(p0 -> (!p1 U (p1 U (!p1 & (p2 R !p1)))))
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p-patterns=8,G(p0 -> (p1 R !p2))
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p-patterns=9,G(!p0 -> Fp0)
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p-patterns=10,G(p0 -> F(p1 | p2))
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p-patterns=11,!(!(p0 | p1) U p2) & G(p3 -> !(!(p0 | p1) U p2))
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p-patterns=12,G!p0 -> G!p1
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p-patterns=13,G(p0 -> (G!p1 | (!p2 U p1)))
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p-patterns=14,G(p0 -> (p1 R (p1 | !p2)))
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p-patterns=15,G((p0 & p1) -> (!p1 R (p0 | !p1)))
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p-patterns=16,G(p0 -> F(p1 & p2))
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p-patterns=17,G(p0 -> (!p1 U (p1 U (p1 & p2))))
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p-patterns=18,G(p0 -> (!p1 U (p1 U (!p1 U (p1 U (p1 & p2))))))
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p-patterns=19,GFp0 -> GFp1
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p-patterns=20,GF(p0 | p1) & GF(p1 | p2)
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sb-patterns=1,p0 U p1
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sb-patterns=2,p0 U (p1 U p2)
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sb-patterns=3,!(p0 U (p1 U p2))
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|
sb-patterns=4,GFp0 -> GFp1
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sb-patterns=5,Fp0 U Gp1
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|
sb-patterns=6,Gp0 U p1
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sb-patterns=7,!(Fp0 <-> Fp1)
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|
sb-patterns=8,!(GFp0 -> GFp1)
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|
sb-patterns=9,!(GFp0 <-> GFp1)
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|
sb-patterns=10,p0 R (p0 | p1)
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sb-patterns=11,(Xp0 U Xp1) | !X(p0 U p1)
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|
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)))
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|
sb-patterns=14,G(p0 -> Fp1) & ((Xp0 U Xp1) | !X(p0 U p1))
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|
sb-patterns=15,G(p0 -> Fp1)
|
|
sb-patterns=16,!G(p0 -> X(p1 R p2))
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sb-patterns=17,!(FGp0 | FGp1)
|
|
sb-patterns=18,G(Fp0 & Fp1)
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|
sb-patterns=19,Fp0 & F!p0
|
|
sb-patterns=20,(p0 & Xp1) R X(((p2 U p3) R p0) U (p2 R p0))
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|
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)
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#+end_example
|
|
|
|
Note that ~--sb-patterns=2 --sb-patterns=4 --sb-patterns=21..22~ also
|
|
have their complement formula listed as ~--sb-patterns=3
|
|
--sb-patterns=8 --sb-patterns=23..24~. So if you build the set of
|
|
formula output by =genltl --sb-patterns= plus its negation, 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:
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|
: 27
|
|
: 46
|
|
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|
# LocalWords: genltl num toc LTL scalable SRC sed gh pn fg FG gf qn
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|
# LocalWords: ccj Xp XXp Xq XXq rv GFp lbt utf SETUPFILE html dac
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|
# LocalWords: Dwyer et al FMSP Etessami Holzmann sb Somenzi Bloem
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|
# LocalWords: CAV LaTeX Fq Fp pNN Gp XFp XF XGp FGp XG ltlfilt uniq
|