#+TITLE: =ltlcross= #+EMAIL spot@lrde.epita.fr #+OPTIONS: H:2 num:nil toc:t #+LINK_UP: file:tools.html =ltlcross= is a tool for cross-comparing the output of LTL-to-Büchi translators. It is actually a Spot-based clone of [[http://www.tcs.hut.fi/Software/lbtt/][LBTT]], the /LTL-to-Büchi Translator Testbench/, that essentially performs the same sanity checks. The main motivations for rewriting this tool were: - support for PSL formulas in addition to LTL - more statistics, especially: - the number of logical transitions represented by each physical edge, - the number of deterministic states and automata - the number of SCCs with their various strengths (nonaccepting, terminal, weak, strong) - the number of terminal, weak, and strong automata - output in a format that can be more easily be post-processed, - more precise time measurement (LBTT was only precise to 1/100 of a second, reporting most times as "0.00s"). Although =ltlcross= performs the same sanity checks as LBTT, it does not implement any of the interactive features of LBTT. In our almost 10-year usage of LBTT, we never had to use its interactive features to understand bugs in our translation. Therefore =ltlcross= will report problems, but you will be on your own to investigate and fix them. The core of =ltlcross= is a loop that does the following steps: - Input a formula - Translate the formula and its negation using each configured translator. If there are 3 translators, the positive and negative translations will be denoted =P0=, =N0=, =P1=, =N1=, =P2=, =N2=. - Build the products of these automata with a random state-space (the same state-space for all translations). (If the =--products=N= option is given, =N= products are performed instead.) - Perform sanity checks between all these automata to detect any problem. - Gather statistics if requested. * Formula selection Formulas to translate should be specified using the [[file:ioltl.org][common input options]]. Standard input is read if no =-f= or =-F= option is given. * Configuring translators Each translator should be specified as a string that use some of the following character sequences: #+BEGIN_SRC sh :results verbatim :exports results ltlcross --help | sed -n '/character sequences:/,/^$/p' | sed '1d;$d' #+END_SRC #+RESULTS: : %f,%s,%l,%w the formula as a (quoted) string in Spot, Spin, : LBT, or Wring's syntax : %F,%S,%L,%W the formula as a file in Spot, Spin, LBT, or : Wring's syntax : %N,%T the output automaton as a Never claim, or in : LBTT's format For instance here is how we could cross-compare the never claims output by =spin= and =ltl2tgba= for the formulas =GFa= and =X(a U b)=. #+BEGIN_SRC sh :results verbatim :exports code ltlcross -f 'GFa' -f 'X(a U b)' 'ltl2tgba -s %s >%N' 'spin -f %s >%N' #+END_SRC #+RESULTS: When =ltlcross= executes these commands, =%s= will be replaced by the formula in Spin's syntax, and =%N= will be replaced by a temporary file into which the output of the translator is redirected before it is read back by =ltlcross=. #+BEGIN_SRC sh :results verbatim :exports results ltlcross -f 'GFa' -f 'X(a U b)' 'ltl2tgba -s %s >%N' 'spin -f %s >%N' 2>&1 #+END_SRC #+RESULTS: #+begin_example ([](<>(a))) Running [P0]: ltl2tgba -s '([](<>(a)))' >'lck-o0-iDGV6y' Running [P1]: spin -f '([](<>(a)))' >'lck-o1-sA3FYp' Running [N0]: ltl2tgba -s '(!([](<>(a))))' >'lck-o0-1ClVQg' Running [N1]: spin -f '(!([](<>(a))))' >'lck-o1-wyErP7' Performing sanity checks and gathering statistics... (X((a) U (b))) Running [P0]: ltl2tgba -s '(X((a) U (b)))' >'lck-o0-ex1BYY' Running [P1]: spin -f '(X((a) U (b)))' >'lck-o1-UNE8dQ' Running [N0]: ltl2tgba -s '(!(X((a) U (b))))' >'lck-o0-coM8tH' Running [N1]: spin -f '(!(X((a) U (b))))' >'lck-o1-eHPoQy' Performing sanity checks and gathering statistics... no problem detected #+end_example =ltlcross= can only read two kinds of output: - Never claims (only if they are restricted to representing an automaton using =if=, =goto=, and =skip= statements) such as those output by [[http://spinroot.com/][=spin=]], [[http://www.lsv.ens-cachan.fr/~gastin/ltl2ba/][=ltl2ba=]], [[http://sourceforge.net/projects/ltl3ba/][=ltl3ba=]], or =ltl2tgba --spin=. These should be indicated using =%N=. - [[http://www.tcs.hut.fi/Software/lbtt/doc/html/Format-for-automata.html][LBTT's format]], which supports generalized Büchi automata with either state-based acceptance or transition-based acceptance. This output is used for instance by [[http://www.tcs.hut.fi/Software/maria/tools/lbt/][=lbt=]], [[http://web.archive.org/web/20080607170403/http://www.science.unitn.it/~stonetta/modella.html][=modella=]], or =ltl2tgba --lbtt=. These should be indicated using =%T=. Of course all configured tools need not the same =%= sequences. * Getting statistics Detailed statistics about the result of each translation, and the product of that resulting automaton with the random state-space, can be obtained using the =--csv=FILE= or =--json=FILE= option. ** CSV or JSON output (or both!) The following compare =ltl2tgba=, =spin=, and =lbt= on three random formula (where =W= and =M= operators have been rewritten away because they are not supported by =spin= and =lbt=). #+BEGIN_SRC sh :results verbatim :exports code randltl -n 2 a b | ltlfilt --remove-wm | ltlcross --csv=results.csv \ 'ltl2tgba -s %f >%N' \ 'spin -f %s >%N' \ 'lbt < %L >%T' #+END_SRC #+RESULTS: #+BEGIN_SRC sh :results verbatim :exports results randltl -n 2 a b c | ltlfilt --remove-wm | ltlcross --csv=results.csv --json=results.json \ 'ltl2tgba -s %f >%N' \ 'spin -f %s >%N' \ 'lbt < %L >%T' --csv=results.csv 2>&1 #+END_SRC #+RESULTS: #+begin_example -:1: (G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1))))) Running [P0]: ltl2tgba -s '(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1)))))' >'lck-o0-HcRzrd' Running [P1]: spin -f '([]((((p0) && (<>(p1))) U ((p1) U ((p1) && ((!(p2)) V (p0))))) V ((((p0) && (<>(p1))) U ((p1) U ((p1) && ((!(p2)) V (p0))))) || (X(p1)))))' >'lck-o1-Sir9YC' Running [P2]: lbt < 'lck-i0-W7LdjO' >'lck-o2-ZACV3b' Running [N0]: ltl2tgba -s '(!(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1))))))' >'lck-o0-KoveKk' Running [N1]: spin -f '(!([]((((p0) && (<>(p1))) U ((p1) U ((p1) && ((!(p2)) V (p0))))) V ((((p0) && (<>(p1))) U ((p1) U ((p1) && ((!(p2)) V (p0))))) || (X(p1))))))' >'lck-o1-xxXdfU' Running [N2]: lbt < 'lck-i0-tcO4oL' >'lck-o2-QQUs0t' Performing sanity checks and gathering statistics... -:2: (!(((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1)))) Running [P0]: ltl2tgba -s '(!(((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))))' >'lck-o0-qlcvic' Running [P1]: spin -f '(!((!(p1)) || (!(((!([]((p0) || (<>(p1))))) && ((p0) || (X(p1)))) || (([]((p0) || (<>(p1)))) && (!((p0) || (X(p1)))))))))' >'lck-o1-fEBqz3' Running [P2]: lbt < 'lck-i1-sint9k' >'lck-o2-6oY4RU' Running [N0]: ltl2tgba -s '((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))' >'lck-o0-6PQGuD' Running [N1]: spin -f '(!(p1)) || (!(((!([]((p0) || (<>(p1))))) && ((p0) || (X(p1)))) || (([]((p0) || (<>(p1)))) && (!((p0) || (X(p1)))))))' >'lck-o1-1l4NVu' Running [N2]: lbt < 'lck-i1-iEEnbM' >'lck-o2-a2Toum' Performing sanity checks and gathering statistics... No problem detected. #+end_example After this execution, the file =results.csv= contains the following: #+BEGIN_SRC sh :results verbatim :exports results cat results.csv #+END_SRC #+RESULTS: #+begin_example "formula", "tool", "states", "edges", "transitions", "acc", "scc", "nonacc_scc", "terminal_scc", "weak_scc", "strong_scc", "nondetstates", "nondeterministic", "terminal_aut", "weak_aut", "strong_aut", "time", "product_states", "product_transitions", "product_scc" "(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1)))))", "ltl2tgba -s %f >%N", 7, 27, 42, 1, 1, 0, 0, 0, 1, 5, 1, 0, 0, 1, 0.162927, 1333, 20565, 3 "(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1)))))", "spin -f %s >%N", 55, 957, 1723, 1, 1, 0, 0, 0, 1, 55, 1, 0, 0, 1, 3.83261, 10791, 866615, 37 "(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1)))))", "lbt < %L >%T", 167, 5656, 10744, 3, 2, 1, 0, 0, 1, 167, 1, 0, 0, 1, 0.0365079, 32258, 5318535, 96 "(!(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1))))))", "ltl2tgba -s %f >%N", 11, 28, 72, 1, 10, 6, 1, 2, 1, 1, 1, 0, 0, 1, 0.0628941, 2163, 36722, 594 "(!(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1))))))", "spin -f %s >%N", 23, 113, 331, 1, 14, 9, 1, 1, 3, 20, 1, 0, 0, 1, 0.101343, 4567, 171114, 1193 "(!(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1))))))", "lbt < %L >%T", 157, 2414, 5957, 3, 109, 103, 1, 1, 4, 133, 1, 0, 0, 1, 0.0197828, 30811, 3020266, 19147 "(!(((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))))", "ltl2tgba -s %f >%N", 6, 12, 21, 1, 5, 3, 0, 1, 1, 1, 1, 0, 0, 1, 0.0509422, 806, 15638, 9 "(!(((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))))", "spin -f %s >%N", 11, 21, 47, 1, 8, 6, 0, 1, 1, 7, 1, 0, 0, 1, 0.0102468, 1217, 36416, 20 "(!(((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))))", "lbt < %L >%T", 17, 45, 100, 2, 13, 11, 0, 1, 1, 14, 1, 0, 0, 1, 0.00346881, 1744, 57783, 347 "((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))", "ltl2tgba -s %f >%N", 7, 14, 28, 1, 6, 3, 1, 1, 1, 2, 1, 0, 0, 1, 0.0503676, 1006, 19822, 10 "((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))", "spin -f %s >%N", 17, 43, 102, 1, 13, 10, 1, 1, 1, 12, 1, 0, 0, 1, 0.0474604, 2449, 70190, 256 "((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))", "lbt < %L >%T", 23, 68, 154, 2, 19, 16, 1, 1, 1, 18, 1, 0, 0, 1, 0.0037305, 2236, 73111, 640 #+end_example This can be loaded in any spreadsheet application. Although we only supplied 2 random generated formulas, the output contains 4 formulas because =ltlcross= had to translate the positive and negative version of each. If we had used the option =--json=results.json= instead of (or in addition to) =--cvs=results.csv=, the file =results.json= would have contained the following [[http://www.json.org/][JSON]] output. #+BEGIN_SRC sh :results verbatim :exports results cat results.json #+END_SRC #+RESULTS: #+begin_example { "tool": [ "ltl2tgba -s %f >%N", "spin -f %s >%N", "lbt < %L >%T" ], "formula": [ "(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1)))))", "(!(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1))))))", "(!(((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))))", "((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))" ], "fields": [ "formula", "tool", "states", "edges", "transitions", "acc", "scc", "nonacc_scc", "terminal_scc", "weak_scc", "strong_scc", "nondetstates", "nondeterministic", "terminal_aut", "weak_aut", "strong_aut", "time", "product_states", "product_transitions", "product_scc" ], "inputs": [ 0, 1 ], "results": [ [ 0, 0, 7, 27, 42, 1, 1, 0, 0, 0, 1, 5, 1, 0, 0, 1, 0.162927, 1333, 20565, 3 ], [ 0, 1, 55, 957, 1723, 1, 1, 0, 0, 0, 1, 55, 1, 0, 0, 1, 3.83261, 10791, 866615, 37 ], [ 0, 2, 167, 5656, 10744, 3, 2, 1, 0, 0, 1, 167, 1, 0, 0, 1, 0.0365079, 32258, 5318535, 96 ], [ 1, 0, 11, 28, 72, 1, 10, 6, 1, 2, 1, 1, 1, 0, 0, 1, 0.0628941, 2163, 36722, 594 ], [ 1, 1, 23, 113, 331, 1, 14, 9, 1, 1, 3, 20, 1, 0, 0, 1, 0.101343, 4567, 171114, 1193 ], [ 1, 2, 157, 2414, 5957, 3, 109, 103, 1, 1, 4, 133, 1, 0, 0, 1, 0.0197828, 30811, 3020266, 19147 ], [ 2, 0, 6, 12, 21, 1, 5, 3, 0, 1, 1, 1, 1, 0, 0, 1, 0.0509422, 806, 15638, 9 ], [ 2, 1, 11, 21, 47, 1, 8, 6, 0, 1, 1, 7, 1, 0, 0, 1, 0.0102468, 1217, 36416, 20 ], [ 2, 2, 17, 45, 100, 2, 13, 11, 0, 1, 1, 14, 1, 0, 0, 1, 0.00346881, 1744, 57783, 347 ], [ 3, 0, 7, 14, 28, 1, 6, 3, 1, 1, 1, 2, 1, 0, 0, 1, 0.0503676, 1006, 19822, 10 ], [ 3, 1, 17, 43, 102, 1, 13, 10, 1, 1, 1, 12, 1, 0, 0, 1, 0.0474604, 2449, 70190, 256 ], [ 3, 2, 23, 68, 154, 2, 19, 16, 1, 1, 1, 18, 1, 0, 0, 1, 0.0037305, 2236, 73111, 640 ] ] } #+end_example Here the =fields= table describes the columns of the =results= table. The =inputs= tables lists the columns that are considered as inputs for the experiments. The values in the columns corresponding to the fields =formula= and =tool= contains indices relative to the =formula= and =tool= tables. This format is more compact when dealing with lots of translators and formulas, because they don't have to be repeated on each line as in the CSV version. JSON data can be easily processed in any language. For instance the following Python3 script averages each column for each tool, and presents the results in a form that can almost be copied into a LaTeX table (the =%= in the tool names have to be taken care of). Note that for simplicity we assume that the first two columns are inputs, instead of reading the =inputs= field. #+BEGIN_SRC python :results output :exports both #!/usr/bin/python3 import json data = json.load(open('results.json')) datacols = range(2, len(data["fields"])) # Index results by tool results = { t:[] for t in range(0, len(data["tool"])) } for l in data["results"]: results[l[1]].append(l) # Average columns for each tool, and display them as a table print("%-18s & count & %s \\\\" % ("tool", " & ".join(data["fields"][2:]))) for i in range(0, len(data["tool"])): c = len(results[i]) sums = ["%6.1f" % (sum([x[j] for x in results[i]])/c) for j in datacols] print("%-18s & %3d & %s \\\\" % (data["tool"][i], c, " & ".join(sums))) #+END_SRC #+RESULTS: : tool & count & states & edges & transitions & acc & scc & nonacc_scc & terminal_scc & weak_scc & strong_scc & nondetstates & nondeterministic & terminal_aut & weak_aut & strong_aut & time & product_states & product_transitions & product_scc \\ : ltl2tgba -s %f >%N & 4 & 7.0 & 20.0 & 40.0 & 1.0 & 5.0 & 3.0 & 0.0 & 1.0 & 1.0 & 2.0 & 1.0 & 0.0 & 0.0 & 1.0 & 0.1 & 1327.0 & 23186.0 & 154.0 \\ : spin -f %s >%N & 4 & 26.0 & 283.0 & 550.0 & 1.0 & 9.0 & 6.0 & 0.0 & 0.0 & 1.0 & 23.0 & 1.0 & 0.0 & 0.0 & 1.0 & 1.0 & 4756.0 & 286083.0 & 376.0 \\ : lbt < %L >%T & 4 & 91.0 & 2045.0 & 4238.0 & 2.0 & 35.0 & 32.0 & 0.0 & 0.0 & 1.0 & 83.0 & 1.0 & 0.0 & 0.0 & 1.0 & 0.0 & 16762.0 & 2117423.0 & 5057.0 \\ The script =bench/ltl2tgba/sum.py= is a more evolved version of the above script that generates two kinds of LaTeX tables. When computing such statistics, you should be aware that inputs for which a tool failed to generate an automaton (e.g. it crashed, or it was killed if you used =ltlcross='s =--timeout= option to limit run time) are not represented in the CSV or JSON files. However data for bogus automata are still included: as shown below =ltlcross= will report inconsistencies between automata as errors, but it does not try to guess who is incorrect. ** Description of the columns =formula= and =tool= contain the formula translated and the command run to translate it. In the CSV, these columns contain the actual text. In the JSON output, these column contains an index into the =formula= and =tool= table declared separately. =states=, =edged=, =transitions=, =acc= are size measures for the automaton that was translated. =acc= counts the number of acceptance sets. When building (degeneralized) Büchi automata, it will always be =1=, so its value is meaningful only when evaluating translations to generalized Büchi automata. =edges= counts the actual number of edges in the graph supporting the automaton; an edge (labeled by a Boolean formula) might actually represent several transitions (each labeled by assignment of all atomic propositions). For instance in an automaton where the atomic proposition are $a$ and $b$, one edge labeled by $a\lor b$ actually represents three transitions $a b$, $a\bar b$, and $\bar a b$. The following picture displays two automata for the LTL formula =a U b=. They both have 2 states and 3 edges, however they differ in the number of transitions (7 versus 8), because the initial self-loop is more constrained in the first automaton. A smaller number of transition is therefore an indication of a more constrained automaton. #+BEGIN_SRC dot :file edges.png :cmdline -Tpng :exports results digraph G { 0 [label="", style=invis, height=0] 0 -> 1 1 [label="A1"] 1 -> 2 [label="b\n"] 1 -> 1 [label="a & !b\n"] 2 [label="B1", peripheries=2] 2 -> 2 [label="1"] 3 [label="", style=invis, height=0] 3 -> 4 4 [label="A2"] 4 -> 5 [label="b\n"] 4 -> 4 [label="a\n"] 5 [label="B2", peripheries=2] 5 -> 5 [label="1"] } #+END_SRC #+RESULTS: [[file:edges.png]] =scc= counts the number of strongly-connected components in the automaton. These SCCs are also partitioned on four sets based on their strengths: - =nonacc_scc= for non-accepting SCCs (such as states A1 and A2 in the previous picture) - =terminal_scc= for SCCs that consist of a single state with an accepting self-loop labeled by true (such as states B1 and B2 in the previous picture) - =weak_scc= for non-terminal SCCs in which all cycles are accepting - and =strong_scc= for accepting SCCs in which some cycles are not accepting. These SCC strengths can be used to compute the strength of the automaton as a whole: - an automaton is terminal if it contains only non-accepting or terminal SCCs, - an automaton is weak if it it contains only non-accepting, terminal, or weak SCCs, - an automaton is strong if it contains at least one strong SCC. This classification is used to fill the =terminal_aut=, =weak_aut=, =strong_aut= columns with Boolean values. Only one of these should contain =1=. We usually prefer terminal automata over weak automata, and weak automata over strong automata, because the emptiness check of terminal (and weak) automata is easier. =nondetstates= counts the number of non-deterministic states in the automaton. =nondeterministic= is a Boolean value indicating if the automaton is not deterministic. For instance in the previous picture showing two automata for =a U b=, the first automaton is deterministic (these two fields will contain 0), while the second automaton contain a nondeterministic state (state A2 has two possible successors for the assignment $ab$) and is therefore not deterministic. =time= obviously contains the time used by the translation. Time is measured with some high-resolution clock when available (that's nanosecond accuracy under Linux), but because translator commands are executed through a shell, it also includes the time to start a shell. (This extra cost apply identically to all translators, so it is not unfair.) Finally, =product_states=, =product_transitions=, and =product_scc= count the number of state, transitions and strongly-connect components in the product that has been built between the translated automaton and a random model. For a given formula, the same random model is of course used against the automata translated by all tools. Comparing the size of these product might give another indication of the "conciseness" of a translated automaton. There is of course a certain "luck factor" in the size of the product. Maybe some translator built a very dumb automaton, with many useless states, in which just a very tiny part is translated concisely. By luck, the random model generated might synchronize with this tiny part only, and ignore the part with all the useless states. A way to lessen this luck factor is to increase the number of products performed against the translated automaton. If option =--products=N= is used, =N= products are builds instead of one, and the fields =product_states=, =product_transitions=, and =product_scc= contain average values. * Detecting problems If a translator exits with a non-zero status code, or fails to output an automaton =ltlcross= can read, and error will be displayed and the result of the translation will be discarded. Otherwise =ltlcross= performs the following checks on all translated formulas ($P_i$ and $N_i$ designate respectively the translation of positive and negative formulas by the ith translator). - Intersection check: $P_i\otimes N_j$ must be empty for all pairs of $(i,j)$. A single failing translator might generate a lot of lines of the form: : error: P0*N1 is nonempty; both automata accept the infinite word : cycle{p0 & !p1} : error: P1*N0 is nonempty; both automata accept the infinite word : p0; !p1; cycle{p0 & p1} : error: P1*N1 is nonempty; both automata accept the infinite word : p0; cycle{!p1 & !p0} : error: P1*N2 is nonempty; both automata accept the infinite word : p0; !p1; cycle{p0 & p1} : error: P1*N3 is nonempty; both automata accept the infinite word : p0; !p1; cycle{p0 & p1} : error: P1*N4 is nonempty; both automata accept the infinite word : p0; cycle{!p1 & !p0} : error: P2*N1 is nonempty; both automata accept the infinite word : p0; !p1; !p0; cycle{!p1 & !p0; p0 & !p1; !p1; !p1; p0 & !p1} : error: P3*N1 is nonempty; both automata accept the infinite word : p0; !p1; !p1 & !p0; cycle{p0 & !p1} : error: P4*N1 is nonempty; both automata accept the infinite word : p0; !p1; !p1 & !p0; cycle{p0 & !p1} In this example, translator number =1= looks clearly faulty (at least the other 4 translators do not contradict each other). Examples of infinite words that are accepted by both automata always have the form of a lasso: a (possibly empty) finite prefix followed by a cycle that should be repeated infinitely often. The cycle part is denoted by =cycle{...}=. - Cross-comparison checks: for some state-space $S$, all $P_i\otimes S$ are either all empty, or all non-empty. Similarly all $N_i\otimes S$ are either all empty, or all non-empty. A cross-comparison failure could be displayed as: : error: {P0,P2,P3,P4,P5,P6,P7,P8,P9} disagree with {P1} when evaluating the state-space If =--products=N= is used with =N= greater than one, the number of the state-space is also printed. This number is of no use by itself, except to explain why you may get multiple disagreement between the same sets of automata. - Consistency check: For each $i$, the products $P_i\otimes S$ and $N_i\otimes S$ actually cover all states of $S$. Because $S$ does not have any deadlock, any of its infinite path must be accepted by $P_i$ or $N_i$ (or both). An error in that case is displayed as : error: inconsistency between P1 and N1 If =--products=N= is used with =N= greater than one, the number of the state-space in which the inconsistency was detected is also printed. The above checks are similar to those that are performed by [[http://www.tcs.hut.fi/Software/lbtt/][LBTT]]. If any problem was reported during the translation of one of the formulas, =ltlcheck= will exit with an exit status of =1=. Statistics (if requested) are output nonetheless, and include any faulty automaton as well. * Miscellaneous options ** =--stop-on-error= The =--stop-on-error= will cause =ltlcross= to abort on the first detected error. This include failure to start some translator, read its output, or failure to passe the sanity checks. Timeouts are allowed. One use for this option is when =ltlcross= is used in combination with =randltl= to check translators on an infinite stream of formulas. For instance the following will cross-compare =ltl2tgba= against =ltl3ba= until it finds an error, or your interrupt the command, or it runs out of memory (the hash tables used by =randltl= and =ltlcross= to remove duplicate formulas will keep growing). #+BEGIN_SRC sh :export code :eval no randltl -n -1 --tree-size 10..25 a b c | ltlcross --stop-on-error 'ltl2tgba --lbtt %f >%T' 'ltl3ba -f %s >%N' #+END_SRC ** =--no-check= The =--no-check= option disables all sanity checks, and only use the supplied formulas in their positive form. When checks are enabled, the negated formulas are intermixed with the positives ones in the results. Therefore the =--no-check= option can be used to gather statistics about a specific set of formulas. # LocalWords: ltlcross num toc LTL Büchi LBTT Testbench PSL SRC sed # LocalWords: automata LBT LBTT's ltl tgba GFa lck iDGV sA FYp BYY # LocalWords: ClVQg wyErP UNE dQ coM tH eHPoQy goto ba lbt modella # LocalWords: lbtt csv json randltl ltlfilt wm eGEYaZ nYpFBX fGdZQ # LocalWords: CPs kXiZZS ILLzR wU CcMCaQ IOckzW tsT RZ TJXmT jb XRO # LocalWords: nxqfd hS vNItGg acc scc nondetstates nondeterministic # LocalWords: cvs LaTeX datacols len ith otimes ltlcheck eval setq # LocalWords: setenv concat getenv