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# `ltldo`

## Table of Contents

- Example: computing statistics for `ltl3ba`
- Example: running `spin` and producing HOA
- Syntax for specifying tools to call
- Shorthands for existing tools
- Transparent renaming
- Acting as a portfolio of translators
- Controlling and measuring time

This tool is a wrapper for tools that read LTL/PSL formulas and (optionally) output automata.

It reads formulas specified using the common options for specifying input and passes each formula to a tool (or a list of tools) specified using options similar to those of `ltlcross`. In case that tool returns an automaton, the resulting automaton is read back by `ltldo` and is finally output as specified using the common options for outputing automata.

In effect, `ltldo` wraps the I/O interface of the Spot tools on top of any other tool.

## Example: computing statistics for `ltl3ba`

As a motivating example, consider a scenario where we want to run `ltl3ba` on a set of 10 formulas stored in a file. For each formula we would like to compute compute the number of states and edges in the Büchi automaton produced by `ltl3ba`.

Here is the input file:

    cat >sample.ltl <<EOF
    1
    1 U a
    !(!((a U Gb) U b) U GFa)
    (b <-> Xc) xor Fb
    FXb R (a R (1 U b))
    Ga
    G(!(c | (a & (a W Gb))) M Xa)
    GF((b R !a) U (Xc M 1))
    G(Xb | Gc)
    XG!F(a xor Gb)
    EOF

We will first implement this scenario without `ltldo`.

A first problem that the input is not in the correct syntax: although `ltl3ba` understands `G` and `F`, it does not support `xor` or `M`, and requires the Boolean operators `||` and `&&`. This syntax issue can be fixed by processing the input with `ltlfilt -s`.

A second problem is that `ltl3ba` (at least version 1.1.1) can only process one formula at a time. So we'll need to call `ltl3ba` in a loop.

Finally, one way to compute the size of the resulting Büchi automaton is to pipe the output of `ltl3ba` through `autfilt`.

Here is how the shell command could look like:

    ltlfilt -F sample.ltl -s |
    while read f; do
      ltl3ba -f "$f" | autfilt --stats="$f,%s,%t"
    done

    true,1,1
    true U a,2,4
    !(!((a U []b) U b) U []<>a),2,4
    !((b <-> Xc) <-> <>b),7,21
    <>Xb V (a V (true U b)),6,28
    []a,1,1
    [](Xa U (Xa && !(c || (a && ([]b V (a || []b)))))),1,0
    []<>((b V !a) U (true U Xc)),2,4
    [](Xb || []c),3,11
    X[]!<>!(a <-> []b),4,10

Using `ltldo` the above command can be reduced to this:

    ltldo 'ltl3ba -f %s>%O' -F sample.ltl --stats='%f,%s,%t'

    1,1,1
    1 U a,2,4
    !(!((a U Gb) U b) U GFa),2,4
    (b <-> Xc) xor Fb,7,21
    FXb R (a R (1 U b)),6,28
    Ga,1,1
    G(!(c | (a & (a W Gb))) M Xa),1,0
    GF((b R !a) U (Xc M 1)),2,4
    G(Xb | Gc),3,11
    XG!F(a xor Gb),4,10

Note that the formulas look different in both cases, because in the `while` loop the formula printed has already been processed with `ltlfilt`, while `ltldo` emits the input string untouched.

In fact, as we will discuss below, `ltl3ba` is a tool that `ltldo` already knows about, so there is a shorter way to run the above command:

    ltldo ltl3ba -F sample.ltl --stats='%f,%s,%t'

## Example: running `spin` and producing HOA

Here is another example, where we use Spin to produce two automata in the HOA format. Spin has no support for HOA, but `ltldo` simply converts the never claim produced by `spin` into this format.

    ltldo -f a -f GFa 'spin -f %s>%O'

    HOA: v1
    States: 2
    Start: 0
    AP: 1 "a"
    acc-name: Buchi
    Acceptance: 1 Inf(0)
    properties: trans-labels explicit-labels state-acc colored
    properties: deterministic
    --BODY--
    State: 0 {0}
    [0] 1
    State: 1 {0}
    [t] 1
    --END--
    HOA: v1
    States: 2
    Start: 0
    AP: 1 "a"
    acc-name: Buchi
    Acceptance: 1 Inf(0)
    properties: trans-labels explicit-labels state-acc complete
    --BODY--
    State: 0
    [0] 1
    [t] 0
    State: 1 {0}
    [t] 0
    --END--

Again, using the shorthands defined below, the previous command can be simplified to just this:

    ltldo spin -f a -f GFa

## Syntax for specifying tools to call

The syntax for specifying how a tool should be called is the same as in `ltlcross`. Namely, the following sequences are available.

    %%                         a single %
    %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
    %O                         the automaton output in HOA, never claim, LBTT, or
                               ltl2dstar's format

Contrarily to `ltlcross`, it this not mandatory to specify an output filename using one of the sequence for that last line. For instance we could simply run a formula though `echo` to compare different output syntaxes:

    ltldo -f 'p0 U p1' -f 'GFp0' 'echo %f, %s, %l, %w'

    (p0) U (p1), (p0) U (p1), U p0 p1, (p0=1) U (p1=1)
    G(F(p0)), [](<>(p0)), G F p0, G(F(p0=1))

In this case (i.e., when the command does not specify any output filename), `ltldo` will not output anything.

As will `ltlcross`, multiple commands can be given, and they will be executed on each formula in the same order.

A typical use-case is to compare statistics of different tools:

    ltldo -F sample.ltl 'spin -f %s>%O' 'ltl3ba -f %s>%O' --stats=%T,%f,%s,%e

    spin -f %s>%O,1,2,2
    ltl3ba -f %s>%O,1,1,1
    spin -f %s>%O,1 U a,2,3
    ltl3ba -f %s>%O,1 U a,2,3
    spin -f %s>%O,!(!((a U Gb) U b) U GFa),23,86
    ltl3ba -f %s>%O,!(!((a U Gb) U b) U GFa),2,3
    spin -f %s>%O,(b <-> Xc) xor Fb,11,19
    ltl3ba -f %s>%O,(b <-> Xc) xor Fb,7,11
    spin -f %s>%O,FXb R (a R (1 U b)),28,176
    ltl3ba -f %s>%O,FXb R (a R (1 U b)),6,20
    spin -f %s>%O,Ga,1,1
    ltl3ba -f %s>%O,Ga,1,1
    spin -f %s>%O,G(!(c | (a & (a W Gb))) M Xa),15,51
    ltl3ba -f %s>%O,G(!(c | (a & (a W Gb))) M Xa),1,0
    spin -f %s>%O,GF((b R !a) U (Xc M 1)),12,60
    ltl3ba -f %s>%O,GF((b R !a) U (Xc M 1)),2,4
    spin -f %s>%O,G(Xb | Gc),4,8
    ltl3ba -f %s>%O,G(Xb | Gc),3,5
    spin -f %s>%O,XG!F(a xor Gb),8,19
    ltl3ba -f %s>%O,XG!F(a xor Gb),4,7

Here we used `%T` to output the name of the tool used to translate the formula `%f` as an automaton with `%s` states and `%e` edges. If you feel that `%T` has too much clutter, you can give each tool a shorter name by prefixing its command with `{name}`.

In the following example, we moved the formula used on its own line using the trick that the command `echo %f` will not be subject to `--stats` (since it does not declare any output automaton).

    ltldo -F sample.ltl  --stats=%T,%s,%e \
          'echo "#" %f' '{spin}spin -f %s>%O' '{ltl3ba}ltl3ba -f %s>%O'

    # 1
    spin,2,2
    ltl3ba,1,1
    # (1) U (a)
    spin,2,3
    ltl3ba,2,3
    # !((!(((a) U (G(b))) U (b))) U (G(F(a))))
    spin,23,86
    ltl3ba,2,3
    # ((b) <-> (X(c))) xor (F(b))
    spin,11,19
    ltl3ba,7,11
    # (F(X(b))) R ((a) R ((1) U (b)))
    spin,28,176
    ltl3ba,6,20
    # G(a)
    spin,1,1
    ltl3ba,1,1
    # G((!((c) | ((a) & ((a) W (G(b)))))) M (X(a)))
    spin,15,51
    ltl3ba,1,0
    # G(F(((b) R (!(a))) U ((X(c)) M (1))))
    spin,12,60
    ltl3ba,2,4
    # G((X(b)) | (G(c)))
    spin,4,8
    ltl3ba,3,5
    # X(G(!(F((a) xor (G(b))))))
    spin,8,19
    ltl3ba,4,7

Much more readable!

## Shorthands for existing tools

There is a list of existing tools for which `ltldo` (and `ltlcross`) have built-in specifications. This list can be printed using the `--list-shorthands` option:

    ltldo --list-shorthands

    If a COMMANDFMT does not use any %-sequence, and starts with one of
    the following words, then the string on the right is appended.

      lbt          <%L>%O
      ltl2ba       -f %s>%O
      ltl2da       %f>%O
      ltl2dpa      %f>%O
      ltl2ldba     %f>%O
      ltl2dstar    --output-format=hoa %[MW]L %O
      ltl2tgba     -H %f>%O
      ltl3ba       -f %s>%O
      ltl3dra      -f %s>%O
      ltl3hoa      -f %f>%O
      modella      %[MWei^]L %O
      spin         -f %s>%O

    Any {name} and directory component is skipped for the purpose of
    matching those prefixes.  So for instance
      '{DRA} ~/mytools/ltl2dstar-0.5.2'
    will changed into
      '{DRA} ~/mytools/ltl2dstar-0.5.2 --output-format=hoa %[MR]L %O'

Therefore you can type just

    ltldo ltl2ba -f a -d

to obtain a Dot output (as requested with `-d`) for the neverclaim produced by `ltl2ba -f a`.

    digraph G {
      rankdir=LR
      node [shape="circle"]
      I [label="", style=invis, width=0]
      I -> 0
      0 [label="0", peripheries=2]
      0 -> 1 [label="a"]
      1 [label="1", peripheries=2]
      1 -> 1 [label="1"]
    }

The `ltl2ba` argument passed to `ltldo` was interpreted as if you had typed `{ltl2ba}ltl2ba -f %s>%O`.

The shorthand is only used if it is the first word of an command string that does not use any `%` character. This makes it possible to add options:

    ltldo ltl3ba 'ltl3ba -H2' -f GFa --stats='%T, %s states, %e edges'

    ltl3ba, 2 states, 4 edges
    ltl3ba -H2, 1 states, 2 edges

## Transparent renaming

If you have ever tried to use `spin`, `ltl2ba`, or `ltl3ba`, to translate a formula such as `[]!Error`, you have noticed that it does not work:

    spin -f '[]!Error'

    tl_spin: expected predicate, saw 'E'
    tl_spin: []!Error
    -------------^

All these tools are based on the same LTL parser, that allows only atomic propositions starting with a lowercase letter.

Running the same command through `ltldo` will work:

    ltldo spin -f '[]!Error' -s

    never {
    accept_init:
      if
      :: (!(Error)) -> goto accept_init
      fi;
    }

(We need the `-s` option to obtain a never claim, instead of the default HOA output.)

What happened is that `ltldo` renamed the atomic propositions in the formula before calling `spin`. So `spin` actually received the formula `[]!p0` and produced a never claim using `p0`. That never claim was then relabeled by `ltldo` to use `Error` instead of `p0`.

This renaming occurs any time some command uses `%s` or `%S` and the formula has atomic propositions incompatible with Spin's conventions; or when some command uses `%l` or `%L`, and the formula has atomic propositions incompatible with LBT's conventions.

For `%f`, `%w`, `%F`, and `%W`, no relabeling is automatically performed, but you can pass option `--relabel` if you need to force it for some reason (e.g., if you have a tool that uses almost Spot's syntax, but cannot cope with double-quoted atomic propositions).

There are some cases where the renaming is not completely transparent. For instance if a translator tool outputs some HOA file named after the formula translated, the name will be output unmodified (since this can be any text string, there is not way for `ltldo` to assume it is an LTL formula). In the following example, you can see that the automaton uses the atomic proposition `Error`, but its name contains a reference to `p0`.

    ltldo 'ltl3ba -H' -f '[]!Error'

    HOA: v1
    name: "BA for [](!(p0))"
    States: 1
    Start: 0
    AP: 1 "Error"
    acc-name: Buchi
    Acceptance: 1 Inf(0)
    properties: trans-labels explicit-labels state-acc colored
    properties: deterministic
    --BODY--
    State: 0 "accept_init" {0}
    [!0] 0
    --END--

If this is a problem, you can always force a new name with the `--name` option:

    ltldo 'ltl3ba -H' -f '[]!Error' --name='BA for %f'

    HOA: v1
    name: "BA for []!Error"
    States: 1
    Start: 0
    AP: 1 "Error"
    acc-name: Buchi
    Acceptance: 1 Inf(0)
    properties: trans-labels explicit-labels state-acc colored
    properties: deterministic
    --BODY--
    State: 0 "accept_init" {0}
    [!0] 0
    --END--

## Acting as a portfolio of translators

Here is a formula on which different translators produce Büchi automata of different sizes (states and edges):

    ltldo ltl2ba ltl3ba 'ltl2tgba -s' -f 'F(a & Xa | FGa)' \
          --stats='%T: %s st. (%n non-det.), %e ed.'

    ltl2ba: 5 st. (2 non-det.), 9 ed.
    ltl3ba: 3 st. (1 non-det.), 4 ed.
    ltl2tgba -s: 3 st. (0 non-det.), 5 ed.

Instead of outputting the result of the translation of each formula by each translator, `ltldo` can also be configured to output the smallest automaton obtained for each formula:

    ltldo ltl2ba ltl3ba 'ltl2tgba -s' -f 'F(a & Xa | FGa)' --smallest

    HOA: v1
    States: 3
    Start: 0
    AP: 1 "a"
    acc-name: Buchi
    Acceptance: 1 Inf(0)
    properties: trans-labels explicit-labels state-acc
    --BODY--
    State: 0
    [t] 0
    [0] 1
    State: 1
    [0] 2
    State: 2 {0}
    [t] 2
    --END--

Therefore, in practice, `ltldo --smallest trans1 trans2 trans3...` acts like a portfolio of translators, always returning the smallest produced automaton.

The sorting criterion can be specified using `--smallest` or `--greatest`, optionally followed by a format string with `%`-sequences. The default criterion is `%s,%e`, so the number of states will be compared first, and in case of equality the number of edges. If we desire the automaton that has the fewest states, and in case of equality the smallest number of non-deterministic states, we can use the following command instead.

    ltldo ltl2ba ltl3ba 'ltl2tgba -s' -f 'F(a & Xa | FGa)' --smallest=%s,%n

    HOA: v1
    name: "F(a & Xa)"
    States: 3
    Start: 0
    AP: 1 "a"
    acc-name: Buchi
    Acceptance: 1 Inf(0)
    properties: trans-labels explicit-labels state-acc complete
    properties: deterministic terminal
    --BODY--
    State: 0
    [!0] 0
    [0] 1
    State: 1
    [!0] 0
    [0] 2
    State: 2 {0}
    [t] 2
    --END--

We can of course apply this on a large number of formulas. For instance here is a more complex pipeline, where we take 11 patterns from Dwyer et al. (FMSP'98), and print which translator among `ltl2ba`, `ltl3ba`, and `ltl2tgba -s` would produce the smallest automaton.

    genltl --dac=10..20 --format=%F:%L,%f |
      ltldo -F-/2 ltl2ba ltl3ba 'ltl2tgba -s' --smallest --stats='%<,%T'

    dac-patterns:10,ltl2ba
    dac-patterns:11,ltl3ba
    dac-patterns:12,ltl2tgba -s
    dac-patterns:13,ltl2tgba -s
    dac-patterns:14,ltl2tgba -s
    dac-patterns:15,ltl2tgba -s
    dac-patterns:16,ltl2ba
    dac-patterns:17,ltl2tgba -s
    dac-patterns:18,ltl2ba
    dac-patterns:19,ltl3ba
    dac-patterns:20,ltl2ba

Note that in case of equality, only the first translator is returned. So when `ltl2ba` is output above, it could be the case that `ltl3ba` or `ltl2tgba -s` are also producing automata of equal size.

To understand the above pipeline, remove the `ltldo` invocation. The `genltl` command outputs this:

    genltl --dac=10..20 --format=%F:%L,%f

    dac-patterns:10,G((p0 & !p1) -> (!p1 U (!p1 & p2)))
    dac-patterns:11,!p0 W (p0 W (!p0 W (p0 W G!p0)))
    dac-patterns:12,Fp0 -> ((!p0 & !p1) U (p0 | ((!p0 & p1) U (p0 | ((!p0 & !p1) U (p0 | ((!p0 & p1) U (p0 | (!p1 U p0)))))))))
    dac-patterns:13,Fp0 -> (!p0 U (p0 & (!p1 W (p1 W (!p1 W (p1 W G!p1))))))
    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))))))))))
    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)))))))))
    dac-patterns:16,Gp0
    dac-patterns:17,Fp0 -> (p1 U p0)
    dac-patterns:18,G(p0 -> Gp1)
    dac-patterns:19,G((p0 & !p1 & Fp1) -> (p2 U p1))
    dac-patterns:20,G((p0 & !p1) -> (p2 W p1))

This is a two-column CSV file where each line is a description of the origin of the formula (`%F:%L`), followed by the formula itself (`%f`). The `ltldo` from the previous pipeline simply takes its input from the second column of its standard input (`-F-/2`), run that formula through the three translator, pick the smallest automaton (`--smallest`), and for this automaton, it display the translator that was used (`%T`) along with the portion of the CSV file that was before the input column (`%<`).

## Controlling and measuring time

The run time of each command can be restricted with the `-T NUM` option. The argument is the maximum number of seconds that each command is allowed to run.

When a timeout occurs a warning is printed on stderr, and no automaton (or statistic) is output by `ltdo` for this specific pair of command/formula. The processing then continue with other formulas and tools. Timeouts are not considered as errors, so they have no effect on the exit status of `ltldo`.

For each command (that does not terminate with a timeout) the runtime can be printed using the `%r` escape sequence. This makes `ltldo` an alternative to `ltlcross` for running benchmarks without any verification.