org: update randltl.org
* doc/org/randltl.org: The first example used to output '1' as only random formula. This is not very sexy.
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Alexandre Duret-Lutz
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1 changed files with 54 additions and 54 deletions
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@ -8,14 +8,18 @@ random LTL formula using atomic propositions supplied on the
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command-line. It can be instructed to generate random Boolean or PSL
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formulas instead, but let us first focus on LTL generation.
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For instance to obtain one random LTL formula over the propositions
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For instance to obtain fave random LTL formula over the propositions
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=a=, =b=, or =c=, use:
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#+BEGIN_SRC sh :results verbatim :exports both
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randltl a b c
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randltl -n5 a b c
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#+END_SRC
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#+RESULTS:
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: G(Gb W (Gb M c))
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: 1
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: !(!((a U Gb) U b) U GFa)
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: GF((b R !a) U (Xc M 1))
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: (b <-> Xc) xor Fb
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: FXb R (a R (1 U b))
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Note that the result does not always use all atomic propositions.
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@ -23,10 +27,14 @@ If you do not care about how the atomic propositions are named,
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you can give a nonnegative number instead:
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#+BEGIN_SRC sh :results verbatim :exports both
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randltl 3
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randltl -n5 3
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#+END_SRC
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#+RESULTS:
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: G(Gp1 W (Gp1 M p2))
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: 1
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: !(!((p0 U Gp1) U p1) U GFp0)
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: GF((p1 R !p0) U (Xp2 M 1))
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: (p1 <-> Xp2) xor Fp1
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: FXp1 R (p0 R (1 U p1))
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The syntax of the formula output can be changed using the
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[[file:ioltl.org][common output options]]:
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@ -49,24 +57,26 @@ like =p0=, =p1=, etc... (Atomic proposition named differently will be
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output by Spot in double-quotes, but this is not supported by LBT.)
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#+BEGIN_SRC sh :results verbatim :exports both
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randltl -l 3
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randltl -8 3
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randltl -s 3
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randltl --wring 3
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randltl -l 12
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randltl -8 12
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randltl -s 12
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randltl --wring 12
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#+END_SRC
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#+RESULTS:
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: G W G p1 M G p1 p2
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: □(□p1 W (□p1 M p2))
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: []((p2 U (p2 && []p1)) V ([]p1 || (p2 U (p2 && []p1))))
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: (G(((p2=1) U ((p2=1) * (G(p1=1)))) R ((G(p1=1)) + ((p2=1) U ((p2=1) * (G(p1=1)))))))
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: V ! X ^ G p4 M p10 F ! p11 V G p3 p5
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: ¬○(□p4⊕(p10 M ◇¬p11)) R (□p3 R p5)
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: !X(([]p4 && !(<>!p11 U (p10 && <>!p11))) || (![]p4 && (<>!p11 U (p10 && <>!p11)))) V ([]p3 V p5)
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: (!(X((G(p4=1)) ^ ((F(p11=0)) U ((p10=1) * (F(p11=0))))))) R ((G(p3=1)) R (p5=1))
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As you might guess from the above result, for a given set of atomic
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propositions (and on the same computer) the generated formula will
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always be the same. This is because each time =randltl= starts, it
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initialize the seed of the random number generator to =0=. This seed
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initializes the seed of the random number generator to =0=. This seed
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can be changed using the =--seed= option. For instance the following
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three commands:
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#+NAME: result-seed
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#+BEGIN_SRC sh :results verbatim :exports both
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randltl a b c
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randltl --seed=123 a b c
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@ -75,25 +85,15 @@ randltl --seed=0 a b c
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Will give three formulas in which the first and last are identical:
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#+RESULTS:
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: G(Gb W (Gb M c))
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: X((c <-> F(a M Xc)) -> a)
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: G(Gb W (Gb M c))
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#+RESULTS: result-seed
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: 1
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: b W 0
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: 1
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When generating random formulas, we usually want large quantity of
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them. Rather than running =randltl= several times with different
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seeds, we can use the =-n= option to specify a number of formulas to
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produce.
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#+BEGIN_SRC sh :results verbatim :exports both
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randltl -n 5 a b c
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#+END_SRC
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#+RESULTS:
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: G(Gb W (Gb M c))
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: !(GFb -> Fa)
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: (((c xor Xc) R c) R Gc) & !c
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: X(1 U Xb) M Fb
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: !XFb U !(Xa W 0)
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produce as seen in the very first example of this page.
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By default =randltl= will never output the same formula twice (this
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can be changed with the =--allow-dups= option), so it may generate
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@ -122,11 +122,11 @@ will be chosen randomly in the range =22..30=.
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randltl -n 5 a b c --tree-size=22..30
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#+END_SRC
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#+RESULTS:
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: ((Fc W 0) M 1) & ((a | XXc) M (b W Fb))
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: (!(c | (a R Xb)) <-> (Xc R (a & c))) -> !a
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: (((b xor c) xor (a U (Gc M c))) | (!b xor (a M b))) W (b & Fc)
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: 0
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: X(Xc R GX(1 U Xb)) & GX(b M Xc)
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: (!b -> ((c xor Fa) W b)) W (!Fb U a)
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: !((c xor Gb) -> !Fb) xor !(Gc M 1)
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: 1
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: (a | ((c | G(!a W (!a W b))) W (b & (c M b)))) <-> (b R c)
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The tree size is just the number of nodes in the syntax tree of the
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formula during its construction. However because Spot automatically
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@ -148,11 +148,11 @@ beware that using =-r= reduces the randomness of the output).
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randltl -n 5 a b c --tree-size=22..30 -r
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#+END_SRC
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#+RESULTS:
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: GFc & ((a | XXc) M Fb)
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: !a | (!c & (!a U X!b)) | (a & c & Xc)
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: 1
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: 0
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: XG(b M Xc)
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: (((!c & Fa) | (c & G!a)) W b) W (G!b U a)
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: ((G!b | (!c & F!b) | (c & Gb)) & GF!c) | (Fb & ((!c & Gb) | (c & F!b)) & FGc)
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: (b R c) | (!a & ((!c & F(a & !b)) M (!c W !b)))
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: XGa
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The generator build the syntax tree recursively from its root, by
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considering all operators that could be used for a given tree size (for
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@ -202,11 +202,11 @@ following example disables 6 operators, and augments the priority of
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randltl -n 5 a b c --ltl-priorities 'xor=0,implies=0,equiv=0,W=0,M=0,X=0,U=3'
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#+END_SRC
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#+RESULTS:
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: F(Fb U (c & Gb))
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: !(Fb U Fa)
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: ((Gc U c) U c) U Fc
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: 0
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: 1
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: 1 U b
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: 0
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: F!((b U !a) U Gc)
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: !b U G(b R c)
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When using =-r= to simplify generated formulas, beware that these
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rewritings may use operators that you disabled during the initial
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@ -224,11 +224,11 @@ weak-fairness formula appended.
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randltl -n 5 a b c --weak-fairness
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#+END_SRC
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#+RESULTS:
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: G(Gb W (Gb M c)) & GFb
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: GFb & !(GFb -> Fa) & GFa
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: GFb & (((c xor Xc) R c) R Gc) & !c
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: GFb & GFa & (X(1 U Xb) M Fb)
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: GFb & (!XFb U !(Xa W 0)) & GFc
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: GFb
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: ((b | XXa) M Ga) & GFa & GFc
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: GFb & GFc & !(!((a U Gb) U b) U GFa)
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: GFb & GFa & GFc & F(!X!b U (!c M 1))
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: GFb & GFa & GFc & Xc
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Boolean formulas may be output with the =-B= option:
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@ -236,11 +236,11 @@ Boolean formulas may be output with the =-B= option:
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randltl -B -n 5 a b c
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#+END_SRC
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#+RESULTS:
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: !a -> !b
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: !(!(a -> (b xor c)) -> !a)
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: !c | (!c xor (c xor (c xor !c)))
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: !b
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: a xor !(!b <-> (!a -> c))
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: b & !b
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: b
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: !c xor (!a xor b)
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: !a -> (!c <-> (b xor !(a xor !b)))
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In that case, priorities should be set with =--boolean-priorities=.
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@ -254,11 +254,11 @@ enabled with =-r=).
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randltl -P -n 5 a b c
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#+END_SRC
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#+RESULTS:
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: G(Gb M ((c & Xb) | (!a M 1)))
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: !(Fa xor X({{c | {a xor !b}}[*]}[]-> Fb))
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: c & Gc
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: 0
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: 1
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: a R c
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: F({[*0] | {{[*0] | a[*]}}[*]}[]-> 0)
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: (a | ((a U c) M a)) M 1
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: 0
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As shown with the =--dump-priorities= output below, tweaking the
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priorities used to generated PSL formulas requires three different
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