# -*- coding: utf-8 -*- #+TITLE: =ltlfilt= #+DESCRIPTION: Spot command-line tool for filtering, transforming, and converting LTL formulas. #+INCLUDE: setup.org #+HTML_LINK_UP: tools.html #+PROPERTY: header-args:sh :results verbatim :exports both This tool is a filter for LTL formulas. (It will also work with PSL formulas.) It can be used to perform a number of tasks. Essentially: - converting formulas from one syntax to another, - transforming formulas, - selecting formulas matching some criterion. * Changing syntaxes Because it read and write formulas, =ltlfilt= accepts all the [[file:ioltl.org][common input and output options]]. Additionally, if no =-f= or =-F= option is specified, and =ltlfilt= will read formulas from the standard input if it is not connected to a terminal. For instance the following will convert two LTL formulas expressed using infix notation (with different names supported for the same operators) and convert it into LBT's syntax. #+BEGIN_SRC sh ltlfilt -l -f 'p1 U (p2 & GFp3)' -f 'X<>[]p4' #+END_SRC #+RESULTS: : U p1 & p2 G F p3 : X F G p4 Conversely, here is how to rewrite formulas expressed using the LBT's Polish notation. Let's take the following four formulas taken from examples distributed with =scheck=: #+BEGIN_SRC sh cat >scheck.ltl<, ->, and xor. If no argument is passed, the subset "eFGiMW^" is used. #+end_example As with [[file:randltl.org][=randltl=]], the =-r= option can be used to simplify formulas. #+BEGIN_SRC sh ltlfilt --lbt-input -F scheck.ltl -r #+END_SRC #+RESULTS: : F!p0 & (F!p1 | G!p3) : p3 | Xp7 | Fp6 : Fp1 & XX(XFp5 U (p0 U XXp3)) : p0 U (p1 & (p0 | p5)) You may notice that operands of n-ary operators such as =&= or =|= can be reordered by =ltlfilt= even when the formula is not changed otherwise. This is because Spot internally order all operands of commutative and associative operators, and that this order depends on the order in which the subformulas are first encountered. Adding transformation options such as =-r= may alter this order. However, this difference is semantically insignificant. Formulas can be easily negated using the =-n= option, rewritten into negative normal form using the =--nnf= option, and the =W= and =M= operators can be rewritten using =U= and =R= using the =--remove-wm= option (note that this is already done when a formula is output in Spin's syntax). Another way to alter formula is to rename the atomic propositions it uses. The =--relabel=abc= will relabel all atomic propositions using letters of the alphabet, while =--relabel=pnn= will use =p0=, =p1=, etc. as in LBT's syntax. #+BEGIN_SRC sh ltlfilt --lbt-input -F scheck.ltl -r --relabel=abc #+END_SRC #+RESULTS: : F!a & (F!b | G!c) : a | Xb | Fc : Fa & XX(XFb U (c U XXd)) : a U (b & (a | c)) Note that the relabeling is reset between each formula: =p3= became =c= in the first formula, but it became =d= in the third. Another use of relabeling is to get rid of complex atomic propositions such as the one shown when [[file:ioltl.org][presenting lenient mode]]: #+BEGIN_SRC sh ltlfilt --lenient --relabel=pnn -f '(a < b) U (process[2]@ok)' #+END_SRC #+RESULTS: : p0 U p1 Finally, there is a second variant of the relabeling procedure that is enabled by =--relabel-bool=abc= or =--relabel-book=pnn=. With this option, Boolean subformulas that do not interfere with other subformulas will be changed into atomic propositions. For instance: #+BEGIN_SRC sh ltlfilt -f '(a & !b) & GF(a & !b) & FG(!c)' --relabel-bool=pnn ltlfilt -f '(a & !b) & GF(a & !b) & FG(!c & a)' --relabel-bool=pnn #+END_SRC #+RESULTS: : p0 & GFp0 & FGp1 : p0 & p1 & GF(p0 & p1) & FG(p0 & p2) In the first formula, the independent =a & !b= and =!c= subformulas were respectively renamed =p0= and =p1=. In the second formula, =a & !b= and =!c & a= are dependent, so they could not be renamed; instead =a=, =!b= and =c= were renamed as =p0=, =p1= and =p2=. This option was originally developed to remove superfluous formulas from benchmarks of LTL translators. For instance the automata generated for =GF(a|b)= and =GF(p0)= should be structurally equivalent: replacing =p0= by =a|b= in the second automaton should turn in into the first automaton, and vice versa. (However algorithms dealing with =GF(a|b)= might be slower because they have to deal with more atomic propositions.) So given a long list of LTL formulas, we can combine =--relabel-bool= and =-u= to keep only one instance of formulas that are equivalent after such relabeling. We also suggest to use =--nnf= so that =!FG(a -> b)= would become =GF(p0)= as well. For instance here are some LTL formulas extracted from an [[http://www.fi.muni.cz/~xrehak/publications/verificationresults.ps.gz][industrial project]]: #+BEGIN_SRC sh ltlfilt --nnf -u --relabel-bool < F !hfe_req) G (lup_sr_valid -> F lup_sr_clean ) G F (hfe_req) reset && X G (!reset) G ( (F hfe_clk) && (F ! hfe_clk) ) G ( (F lup_clk) && (F ! lup_clk) ) G F (lup_sr_clean) G ( ( !(lup_addr_5_ <-> (X lup_addr_5_)) || !(lup_addr_6_ <-> (X lup_addr_6_)) || !(lup_addr_7_ <-> (X lup_addr_7_)) || !(lup_addr_8_ <-> (X lup_addr_8_)) ) -> ( (X !lup_sr_clean) && X ( (!( !(lup_addr_5_ <-> (X lup_addr_5_)) || !(lup_addr_6_ <-> (X lup_addr_6_)) || !(lup_addr_7_ <-> (X lup_addr_7_)) || !(lup_addr_8_ <-> (X lup_addr_8_)) )) U lup_sr_clean ) ) ) G F ( !(lup_addr_5_ <-> (X lup_addr_5_)) || !(lup_addr_6_ <-> (X lup_addr_6_)) || !(lup_addr_7_ <-> (X lup_addr_7_)) || !(lup_addr_8_ <-> (X lup_addr_8_)) ) (lup_addr_8__5__eq_0) ((hfe_block_0__eq_0)&&(hfe_block_1__eq_0)&&(hfe_block_2__eq_0)&&(hfe_block_3__eq_0)) G ((lup_addr_8__5__eq_0) -> X( (lup_addr_8__5__eq_0) || (lup_addr_8__5__eq_1) ) ) G ((lup_addr_8__5__eq_1) -> X( (lup_addr_8__5__eq_1) || (lup_addr_8__5__eq_2) ) ) G ((lup_addr_8__5__eq_2) -> X( (lup_addr_8__5__eq_2) || (lup_addr_8__5__eq_3) ) ) G ((lup_addr_8__5__eq_3) -> X( (lup_addr_8__5__eq_3) || (lup_addr_8__5__eq_4) ) ) G ((lup_addr_8__5__eq_4) -> X( (lup_addr_8__5__eq_4) || (lup_addr_8__5__eq_5) ) ) G ((lup_addr_8__5__eq_5) -> X( (lup_addr_8__5__eq_5) || (lup_addr_8__5__eq_6) ) ) G ((lup_addr_8__5__eq_6) -> X( (lup_addr_8__5__eq_6) || (lup_addr_8__5__eq_7) ) ) G ((lup_addr_8__5__eq_7) -> X( (lup_addr_8__5__eq_7) || (lup_addr_8__5__eq_8) ) ) G ((lup_addr_8__5__eq_8) -> X( (lup_addr_8__5__eq_8) || (lup_addr_8__5__eq_9) ) ) G ((lup_addr_8__5__eq_9) -> X( (lup_addr_8__5__eq_9) || (lup_addr_8__5__eq_10) ) ) G ((lup_addr_8__5__eq_10) -> X( (lup_addr_8__5__eq_10) || (lup_addr_8__5__eq_11) ) ) G ((lup_addr_8__5__eq_11) -> X( (lup_addr_8__5__eq_11) || (lup_addr_8__5__eq_12) ) ) G ((lup_addr_8__5__eq_12) -> X( (lup_addr_8__5__eq_12) || (lup_addr_8__5__eq_13) ) ) G ((lup_addr_8__5__eq_13) -> X( (lup_addr_8__5__eq_13) || (lup_addr_8__5__eq_14) ) ) G ((lup_addr_8__5__eq_14) -> X( (lup_addr_8__5__eq_14) || (lup_addr_8__5__eq_15) ) ) G ((lup_addr_8__5__eq_15) -> X( (lup_addr_8__5__eq_15) || (lup_addr_8__5__eq_0) ) ) G (((X hfe_clk) -> hfe_clk)->((hfe_req->X hfe_req)&&((!hfe_req) -> (X !hfe_req)))) G (((X lup_clk) -> lup_clk)->((lup_sr_clean->X lup_sr_clean)&&((!lup_sr_clean) -> (X !lup_sr_clean)))) EOF #+END_SRC #+RESULTS: : G(a | Fb) : GFa : a & XG!a : G(Fa & F!a) : G((((!a & X!a) | (a & Xa)) & ((!b & X!b) | (b & Xb)) & ((!c & X!c) | (c & Xc)) & ((!d & X!d) | (d & Xd))) | (X!e & X((((!a & X!a) | (a & Xa)) & ((!b & X!b) | (b & Xb)) & ((!c & X!c) | (c & Xc)) & ((!d & X!d) | (d & Xd))) U e))) : GF((!a & Xa) | (a & X!a) | (!b & Xb) | (b & X!b) | (!c & Xc) | (c & X!c) | (!d & Xd) | (d & X!d)) : a : G(!a | X(a | b)) : G((!b & Xb) | ((!a | Xa) & (a | X!a))) Here 29 formulas were reduced into 9 formulas after relabeling of Boolean subexpression and removing of duplicate formulas. In other words the original set of formulas contains 9 different patterns. An option that can be used in combination with =--relabel= or =--relabel-bool= is =--define=. This causes the correspondence between old and new names to be printed as a set of =#define= statements. #+BEGIN_SRC sh ltlfilt -f '(a & !b) & GF(a & !b) & FG(!c)' --relabel-bool=pnn --define --spin #+END_SRC #+RESULTS: : #define p0 (a && !b) : #define p1 (!c) : p0 && []<>p0 && <>[]p1 This can be used for instance if you want to use some complex atomic propositions with third-party translators that do not understand them. For instance the following sequence show how to use =ltl3ba= to create a neverclaim for an LTL formula containing atomic propositions that =ltl3ba= cannot parse: #+BEGIN_SRC sh ltlfilt -f '"proc@loc1" U "proc@loc2"' --relabel=pnn --define=ltlex.def --spin | ltl3ba -F - >ltlex.never cat ltlex.def ltlex.never #+END_SRC #+RESULTS: #+begin_example #define p0 ((proc@loc1)) #define p1 ((proc@loc2)) never { /* p0 U p1 */ T0_init: if :: (!p1 && p0) -> goto T0_init :: (p1) -> goto accept_all fi; accept_all: skip } #+end_example As a side note, the tool [[file:ltldo.org][=ltldo=]] might be a simpler answer to this syntactic problem: #+BEGIN_SRC sh ltldo ltl3ba -f '"proc@loc1" U "proc@loc2"' --spin #+END_SRC #+RESULTS: : never { : T0_init: : if : :: ((proc@loc1) && (!(proc@loc2))) -> goto T0_init : :: ((proc@loc2)) -> goto accept_all : fi; : accept_all: : skip : } This case also relabels the formula before calling =ltl3ba=, and it then renames all the atomic propositions in the output. A special relabeling mode related to LTL synthesis is =--relabel=io=. In LTL synthesis (see [[file:ltlsynt.org][=ltlsynt=]]), atomic propositions are partitioned in two sets: the /input/ propositions represent choices from the environment, while /output/ proposition represent choices by the controller to be synthesized. For instance =G(req -> Fack) & G(go -> Fgrant)= represents could be a specification where =req= and =go= are inputs, while =ack= and =grant= are outputs. Tool such as =ltlsynt= need to be told using options such as =--ins= or =--outs= which atomic propositions are input or output. Often these atomic propositions can have very long names, so it is useful to be able to rename them without fogeting about their nature. Option =--relabel=io= combined with one if =--ins= or =--outs= will do exactly that: #+BEGIN_SRC sh ltlfilt -f 'G(req -> Fack) & G(go -> Fgrant)' --relabel=io --ins=req,go #+END_SRC #+RESULTS: : G(i1 -> Fo1) & G(i0 -> Fo0) Like in [[file:ltlsynt.org][=ltlsynt=]], options =--ins= and =--outs= take a comma-separated list of atomic propositions as argument. Additionally, if an atomic proposition in this list is enclosed in slashes (as in =--out=req,/^go/=), it is used as a regular expression for matching atomic propositions. By the way, such an IO-renamed formula can be given to [[file:ltlsynt.org][=ltlsynt=]] without having to specify =--ins= or =--outs=, because when these two options are missing the convention is that anything starting with =i= is an input, and anything starting with =o= is an output. An example showing how to use the =--from-ltlf= option is on [[file:tut12.org][a separate page]]. * Filtering =ltlfilt= supports many ways to filter formulas: #+BEGIN_SRC sh :exports results ltlfilt --help | sed -n '/Filtering options.*:/,/^$/p' | sed '1d;$d' #+END_SRC #+RESULTS: #+begin_example --accept-word=WORD keep formulas that accept WORD --ap=RANGE match formulas with a number of atomic propositions in RANGE --boolean match Boolean formulas --bsize=RANGE match formulas with Boolean size in RANGE --equivalent-to=FORMULA match formulas equivalent to FORMULA --eventual match pure eventualities --guarantee match guarantee formulas (even pathological) --implied-by=FORMULA match formulas implied by FORMULA --imply=FORMULA match formulas implying FORMULA --liveness match liveness properties --ltl match only LTL formulas (no PSL operator) -N, --nth=RANGE assuming input formulas are numbered from 1, keep only those in RANGE --obligation match obligation formulas (even pathological) --persistence match persistence formulas (even pathological) --recurrence match recurrence formulas (even pathological) --reject-word=WORD keep formulas that reject WORD --safety match safety formulas (even pathological) --size=RANGE match formulas with size in RANGE --stutter-insensitive, --stutter-invariant match stutter-insensitive LTL formulas --suspendable synonym for --universal --eventual --syntactic-guarantee match syntactic-guarantee formulas --syntactic-obligation match syntactic-obligation formulas --syntactic-persistence match syntactic-persistence formulas --syntactic-recurrence match syntactic-recurrence formulas --syntactic-safety match syntactic-safety formulas --syntactic-stutter-invariant, --nox match stutter-invariant formulas syntactically (LTL-X or siPSL) --universal match purely universal formulas -u, --unique drop formulas that have already been output (not affected by -v) -v, --invert-match select non-matching formulas #+end_example Most of the above options should be self-explanatory. For instance the following command will extract all formulas from =scheck.ltl= which do not represent guarantee properties. #+BEGIN_SRC sh ltlfilt --lbt-input -F scheck.ltl -v --guarantee #+END_SRC #+RESULTS: : !(Gp0 | (Gp1 & Fp3)) Combining =ltlfilt= with [[file:randltl.org][=randltl=]] makes it easier to generate random formulas that respect certain constraints. For instance let us generate 10 formulas that are equivalent to =a U b=: #+BEGIN_SRC sh randltl -n -1 a b | ltlfilt --equivalent-to 'a U b' -n 10 #+END_SRC #+RESULTS: #+begin_example a U b (b W Fb) & ((Fb xor (a W b)) -> (a U b)) (b U (a W b)) U b !(!b W (!a & !b)) (a M (a <-> (a xor !a))) U b (a U b) | ((a & Xa) M Gb) (a | b) U b (b xor !b) -> ((b W a) U b) (!a -> ((a W b) W (a & b))) U b (a U b) | (Ga U b) #+end_example The =-n -1= option to =randltl= will cause it to output an infinite stream of random formulas. =ltlfilt=, which reads its standard input by default, will select only those equivalent to =a U b=. The output of =ltlfilt= is limited to 10 formulas using =-n 10=. (As would using =| head -n 10=.) Less trivial formulas could be obtained by adding the =-r= option to =randltl= (or equivalently adding the =-r= and =-u= option to =ltlfilt=). Another similar example, that requires two calls to =ltlfilt=, is the generation of random pathological safety formulas. Pathological safety formulas are safety formulas that do not /look/ so syntactically. We can generate some starting again with =randltl=, then ignoring all syntactic safety formulas, and keeping only the safety formulas in the remaining list. #+BEGIN_SRC sh randltl -r -n -1 a b | ltlfilt -v --syntactic-safety | ltlfilt --safety -n 10 #+END_SRC #+RESULTS: #+begin_example G(!b | Gb | X(b & Fa)) ((!a | X(!a R (!b U !a))) & X((!a & !b) | (a & b))) | (a & X(((!a & b) | (a & !b)) & (b R a))) (F!a & (a | G!a)) R Xa (b M XGb) W XXa G(Xa & (!a U G!b)) (a & F!a) R X(a | b) !a | (a & (a M !b)) b U XGb (!a | (a R (!a | Xa))) M X!a Ga | (!b U !a) #+end_example =ltlfilt='s filtering ability can also be used to answer questions about a single formula. For instance is =a U (b U a)= equivalent to =b U a=? #+BEGIN_SRC sh ltlfilt -f 'a U (b U a)' --equivalent-to 'b U a' #+END_SRC #+RESULTS: : a U (b U a) The command prints the formula and returns an exit status of 0 if the two formulas are equivalent. It would print nothing and set the exit status to 1, were the two formulas not equivalent. Is the formula =F(a & X(!a & Gb))= stutter-invariant? #+BEGIN_SRC sh ltlfilt -f 'F(a & X(!a & Gb))' --stutter-invariant #+END_SRC #+RESULTS: : F(a & X(!a & Gb)) Yes it is. And since it is stutter-invariant, there exist some equivalent formulas that do not use =X= operator. The =--remove-x= option gives one: #+BEGIN_SRC sh ltlfilt -f 'F(a & X(!a & Gb))' --remove-x #+END_SRC #+RESULTS: : F(a & ((a & (a U (!a & Gb)) & ((!b U !a) | (b U !a))) | (!a & (!a U (a & !a & Gb)) & ((!b U a) | (b U a))) | (b & (b U (!a & Gb & !b)) & ((!a U !b) | (a U !b))) | (!b & (!b U (!a & b & Gb)) & ((!a U b) | (a U b))) | (!a & Gb & (G!a | Ga) & (Gb | G!b)))) We could even verify that the resulting horrible formula is equivalent to the original one: #+BEGIN_SRC sh ltlfilt -f 'F(a & X(!a & Gb))' --remove-x | ltlfilt --equivalent-to 'F(a & X(!a & Gb))' #+END_SRC #+RESULTS: : F(a & ((a & (a U (!a & Gb)) & ((!b U !a) | (b U !a))) | (!a & (!a U (a & !a & Gb)) & ((!b U a) | (b U a))) | (b & (b U (!a & Gb & !b)) & ((!a U !b) | (a U !b))) | (!b & (!b U (!a & b & Gb)) & ((!a U b) | (a U b))) | (!a & Gb & (G!a | Ga) & (Gb | G!b)))) It is therefore equivalent (otherwise the output would have been empty). The difference between =--size= and =--bsize= lies in the way Boolean subformula are counted. With =--size= the size of the formula is exactly the number of atomic propositions and operators used. For instance the following command generates 10 random formulas with size 5 (the reason [[file:randltl.org][=randltl=]] uses =--tree-size=8= is because the "tree" of the formula generated randomly can be reduced by trivial simplifications such as =!!f= being rewritten to =f=, yielding formulas of smaller sizes). #+BEGIN_SRC sh randltl -n -1 --tree-size=8 a b | ltlfilt --size=5 -n 10 #+END_SRC #+RESULTS: #+begin_example !F!Ga X!(a U b) !G(a & b) (b W a) W 0 b R X!b GF!Xa Xb & Ga a xor !Fb a xor FXb !(0 R Fb) #+end_example With =--bsize=, any Boolean subformula is counted as "1" in the total size. So =F(a & b & c)= would have Boolean-size 2. This type of size is probably a better way to classify formulas that are going to be translated as automata, since transitions are labeled by Boolean formulas: the complexity of the Boolean subformulas has little influence on the overall translation. Here are 10 random formulas with Boolean-size 5: #+BEGIN_SRC sh randltl -n -1 --tree-size=12 a b | ltlfilt --bsize=5 -n 10 #+END_SRC #+RESULTS: #+begin_example Gb xor Fa FX!Fa !(Fb U b) (a -> !b) & XFb X(b & Xb) 0 R (a U !b) XXa R !b (!a & !(!a xor b)) xor (0 R b) GF(1 U b) (a U b) R b #+end_example * Using =--format= and =--output= The =--format= option can be used the alter the way formulas are output. The list of supported =%=-escape sequences are recalled in the =--help= output: #+BEGIN_SRC sh :exports results ltlfilt --help | sed -n '/ sequences:/,/^$/p' | sed '1d;$d' #+END_SRC #+RESULTS: #+begin_example %< the part of the line before the formula if it comes from a column extracted from a CSV file %> the part of the line after the formula if it comes from a column extracted from a CSV file %% a single % %b the Boolean-length of the formula (i.e., all Boolean subformulas count as 1) %f the formula (in the selected syntax) %F the name of the input file %h, %[vw]h the class of the formula is the Manna-Pnueli hierarchy ([v] replaces abbreviations by class names, [w] for all compatible classes) %l the serial number of the output formula %L the original line number in the input file %[OP]n the nesting depth of operator OP. OP should be a single letter denoting the operator to count, or multiple letters to fuse several operators during depth evaluation. Add '~' to rewrite the formula in negative normal form before counting. %r wall-clock time elapsed in seconds (excluding parsing) %R, %[LETTERS]R CPU time (excluding parsing), in seconds; Add LETTERS to restrict to (u) user time, (s) system time, (p) parent process, or (c) children processes. %s the length (or size) of the formula %x, %[LETTERS]X, %[LETTERS]x number of atomic propositions used in the formula; add LETTERS to list atomic propositions with (n) no quoting, (s) occasional double-quotes with C-style escape, (d) double-quotes with C-style escape, (c) double-quotes with CSV-style escape, (p) between parentheses, any extra non-alphanumeric character will be used to separate propositions #+end_example As a trivial example, use #+HTML: --latex --format='$%f$' to enclose formula in LaTeX format with =$...$=. But =--format= can be useful in more complex scenarios. For instance, you could print only the line numbers containing formulas matching some criterion. In the following, we print only the numbers of the lines of =scheck.ltl= that contain guarantee formulas: #+BEGIN_SRC sh ltlfilt --lbt-input -F scheck.ltl --guarantee --format=%L #+END_SRC #+RESULTS: : 2 : 3 : 4 We could also prefix each formula by its size, in order to sort the file by formula size: #+BEGIN_SRC sh ltlfilt --lbt-input scheck.ltl --format='%s,%f' | sort -n #+END_SRC #+RESULTS: : 7,p0 U (p1 & (p0 | p5)) : 7,p3 | Xp7 | Fp6 : 9,!(Gp0 | (Gp1 & Fp3)) : 20,((Xp0 & Xp4) U Fp1) & XX(XFp5 U (p0 U XXp3)) [[file:csv.org][More examples of how to use =--format= to create CSV files are on a separate page]] The =--output= option interprets its argument as an output filename, but after evaluating the =%=-escape sequence for each formula. This makes it very easy to partition a list of formulas in different files. For instance here is how to split =scheck.ltl= according to formula sizes. #+BEGIN_SRC sh ltlfilt --lbt-input scheck.ltl --output='scheck-%s.ltl' wc -l scheck*.ltl #+END_SRC #+RESULTS: : 1 scheck-20.ltl : 2 scheck-7.ltl : 1 scheck-9.ltl : 4 scheck.ltl : 8 total #+BEGIN_SRC sh :results silent :exports results rm -f ltlex.def ltlex.never scheck.ltl #+END_SRC # LocalWords: ltlfilt num toc LTL PSL syntaxes LBT's SRC GFp scheck # LocalWords: ltl EOF lbt Gp Fp Xp XFp XXp randltl ary nnf wm abc # LocalWords: pnn Xb Fc XFb XXd sed boolean bsize nox Gb Fb Xa XGb # LocalWords: XF XXa utf html args isop bool ap APs ltlf LTLf STR # LocalWords: subexpressions unabbreviate substring eFGiMRW eFGiMW # LocalWords: GF FG FGp hfe rdy req lup sr clk addr eq GFa XG Xc Xd # LocalWords: subexpression ba neverclaim ltlex init fi ltldo siPSL # LocalWords: subformula FXb FX CSV vw Pnueli LaTeX wc