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# Common output options for automata

## Table of Contents

- Common output options
- HOA output
- LBTT output
- Spin output
- Dot output
  - Converting dot output to images or pdf
  - Customizing the dot output
  - SVG and CSS
  - Working with `dot2tex`
- Statistics
- Timing
- Naming automata
- Naming output

Spot supports different output syntaxes for automata. This page documents the options, common to all tools where it makes sense, that are used to specify how to output of automata.

## Common output options

All tools that can output automata implement the following options:

    -8, --utf8                 enable UTF-8 characters in output (ignored with
                               --lbtt or --spin)
        --check[=PROP]         test for the additional property PROP and output
                               the result in the HOA format (implies -H).  PROP
                               may be some prefix of 'all' (default),
                               'unambiguous', 'stutter-invariant',
                               'stutter-sensitive-example', 'semi-determinism',
                               or 'strength'.
    -d, --dot[=1|a|A|b|B|c|C(COLOR)|e|E|f(FONT)|h|i(ID)|k|K|n|N|o|r|R|s|t|u|v|y|+INT|<INT|#]
                               GraphViz's format.  Add letters for (1) force
                               numbered states, (a) show acceptance condition
                               (default), (A) hide acceptance condition, (b)
                               acceptance sets as bullets, (B) bullets except for
                               Büchi/co-Büchi automata, (c) force circular
                               nodes, (C) color nodes with COLOR, (d) show
                               origins when known, (e) force elliptic nodes, (E)
                               force rEctangular nodes, (f(FONT)) use FONT, (g)
                               hide edge labels, (h) horizontal layout, (i) or
                               (i(GRAPHID)) add IDs, (k) use state labels when
                               possible, (K) use transition labels (default), (n)
                               show name, (N) hide name, (o) ordered transitions,
                               (r) rainbow colors for acceptance sets, (R) color
                               acceptance sets by Inf/Fin, (s) with SCCs, (t)
                               force transition-based acceptance, (u) hide true
                               states, (v) vertical layout, (y) split universal
                               edges by color, (+INT) add INT to all set numbers,
                               (<INT) display at most INT states, (#) show
                               internal edge numbers
    -H, --hoaf[=1.1|i|k|l|m|s|t|v]   Output the automaton in HOA format
                               (default).  Add letters to select (1.1) version
                               1.1 of the format, (i) use implicit labels for
                               complete deterministic automata, (s) prefer
                               state-based acceptance when possible [default],
                               (t) force transition-based acceptance, (m) mix
                               state and transition-based acceptance, (k) use
                               state labels when possible, (l) single-line
                               output, (v) verbose properties
        --lbtt[=t]             LBTT's format (add =t to force transition-based
                               acceptance even on Büchi automata)
        --name=FORMAT          set the name of the output automaton
    -o, --output=FORMAT        send output to a file named FORMAT instead of
                               standard output.  The first automaton sent to a
                               file truncates it unless FORMAT starts with '>>'.
    -q, --quiet                suppress all normal output
    -s, --spin[=6|c]           Spin neverclaim (implies --ba).  Add letters to
                               select (6) Spin's 6.2.4 style, (c) comments on
                               states
        --stats=FORMAT, --format=FORMAT
                               output statistics about the automaton

The main three output formats (that can also been used as input to some of the tools) are HOA (used by default, or with `-H` or `--hoaf`), LBTT (activated by `--lbtt`), or Spin never claims (activated by `-s` or `--spin`). These three formats also support streaming, i.e., you can concatenate multiple automata (and even mix these three formats in the same stream), and the tools will be able to read and process them in sequence.

The other possible outputs are GraphViz output (`-d` or `--dot`), various statistics (`--stats`), or nothing at all (`--quiet`). It may seem strange to ask a tool to not output anything, but it makes sense when only the exit status matters (for instance using `autfilt` to check whether an input automaton has some property) or for timing purposes.

## HOA output

Details about supported features of the HOA format can be found on a separate page.

The HOA output should be the preferred format to use if you want to pass automata between different tools. Since Spot 1.99.7, it is the default output format, but you can explicitly request it using the `-H` parameter and this allows passing additional options to the HOA printer.

Here is an example where `ltl2tgba` is used to construct two automata: one for `a U b` and one for `(Ga -> Gb) W c`.

    ltl2tgba 'a U b' '(Ga -> Gb) W c'

    HOA: v1
    name: "a U b"
    States: 2
    Start: 1
    AP: 2 "a" "b"
    acc-name: Buchi
    Acceptance: 1 Inf(0)
    properties: trans-labels explicit-labels state-acc deterministic
    properties: stutter-invariant terminal
    --BODY--
    State: 0 {0}
    [t] 0
    State: 1
    [1] 0
    [0&!1] 1
    --END--
    HOA: v1
    name: "(Gb | F!a) W c"
    States: 5
    Start: 0
    AP: 3 "b" "a" "c"
    acc-name: Buchi
    Acceptance: 1 Inf(0)
    properties: trans-labels explicit-labels trans-acc stutter-invariant
    --BODY--
    State: 0
    [!1&!2] 0 {0}
    [2] 1
    [1&!2] 2
    [0&1&!2] 3
    State: 1
    [t] 1 {0}
    State: 2
    [!1&!2] 0 {0}
    [!1&2] 1
    [1&!2] 2
    [1&2] 4
    State: 3
    [0] 3 {0}
    State: 4
    [!1] 1
    [1] 4
    --END--

The above output contains two automata, named after the formulas they represent. Here is a picture of these two automata:

The HOA format supports both state and transition-based acceptance. Although Spot works only with transition-based acceptance, its output routines default to state-based acceptance whenever possible (this is the case in the first of these two automata) and use transition-based acceptance otherwise. You can change this behavior using `-Hs` (or `--hoaf=s`), `-Ht`, or `-Hm`. Option `s` corresponds to the default to use state-based acceptance whenever possible. Option `t` forces transition-based acceptance. For instance compare this output to the previous one:

    ltl2tgba -Ht 'a U b'

    HOA: v1
    name: "a U b"
    States: 2
    Start: 1
    AP: 2 "a" "b"
    acc-name: Buchi
    Acceptance: 1 Inf(0)
    properties: trans-labels explicit-labels trans-acc deterministic
    properties: stutter-invariant terminal
    --BODY--
    State: 0
    [t] 0 {0}
    State: 1
    [1] 0
    [0&!1] 1
    --END--

Option `m` uses mixed acceptance, i.e, some states might use state-based acceptance while other will not:

    ltl2tgba -Hm '(Ga -> Gb) W c'

    HOA: v1
    name: "(Gb | F!a) W c"
    States: 5
    Start: 0
    AP: 3 "b" "a" "c"
    acc-name: Buchi
    Acceptance: 1 Inf(0)
    properties: trans-labels explicit-labels stutter-invariant
    --BODY--
    State: 0
    [!1&!2] 0 {0}
    [2] 1
    [1&!2] 2
    [0&1&!2] 3
    State: 1 {0}
    [t] 1
    State: 2
    [!1&!2] 0 {0}
    [!1&2] 1
    [1&!2] 2
    [1&2] 4
    State: 3 {0}
    [0] 3
    State: 4
    [!1] 1
    [1] 4
    --END--

It is also possible to output each automaton on a single line, in case the result should be used with line-based tools or embedded into a CSV file… Here is an example using both transition-based acceptance, and single-line output:

    ltl2tgba -Htl 'a U b' '(Ga -> Gb) W c'

    HOA: v1 name: "a U b" States: 2 Start: 1 AP: 2 "a" "b" acc-name: Buchi Acceptance: 1 Inf(0) properties: trans-labels explicit-labels trans-acc deterministic stutter-invariant terminal --BODY-- State: 0 [t] 0 {0} State: 1 [1] 0 [0&!1] 1 --END--
    HOA: v1 name: "(Gb | F!a) W c" States: 5 Start: 0 AP: 3 "b" "a" "c" acc-name: Buchi Acceptance: 1 Inf(0) properties: trans-labels explicit-labels trans-acc stutter-invariant --BODY-- State: 0 [!1&!2] 0 {0} [2] 1 [1&!2] 2 [0&1&!2] 3 State: 1 [t] 1 {0} State: 2 [!1&!2] 0 {0} [!1&2] 1 [1&!2] 2 [1&2] 4 State: 3 [0] 3 {0} State: 4 [!1] 1 [1] 4 --END--

Finally, version 1.1 of the HOA format can be specified using the `-H1.1` option. Version 1, which is currently the default, can also be requested explicitly using `-H1`. The main advantage of version 1.1, as far as Spot is concerned, is that some of negated properties can be transmitted. For instance, compare

    ltl2tgba -f GFa -f FGa -H1 --check | grep -E '^(HOA|properties|name):'

    HOA: v1
    name: "GFa"
    properties: trans-labels explicit-labels trans-acc complete
    properties: deterministic stutter-invariant
    HOA: v1
    name: "FGa"
    properties: trans-labels explicit-labels state-acc semi-deterministic
    properties: stutter-invariant very-weak

versus

    ltl2tgba -f GFa -f FGa -H1.1 --check | grep -E '^(HOA|properties|name):'

    HOA: v1.1
    name: "GFa"
    properties: trans-labels explicit-labels trans-acc complete
    properties: deterministic stutter-invariant !inherently-weak
    HOA: v1.1
    name: "FGa"
    properties: trans-labels explicit-labels state-acc !complete
    properties: !deterministic exist-branch !unambiguous semi-deterministic
    properties: stutter-invariant very-weak !terminal

The `--check` option inspects the automata for additional properties such that their strength or whether they are stutter-invariant and unambiguous. You can see in this example that version 1.1 of the format carries additional negated properties that could not be represented in the first version.

## LBTT output

The LBTT output has two flavors: state-based or transition-based. The transition flavor can be recognized by the present of a `t` after the second number. (The first number is the number of states, while the second number is the number of acceptance sets used.)

Compare the following transition-based and state-based Büchi automata for `GFp0`:

    ltl2tgba -b --lbtt 'GFp0'

    1 1t
    0 1
    0 -1 ! p0
    0 0 -1 p0
    -1

    ltl2tgba -B --lbtt 'GFp0'

    2 1
    0 1 0 -1
    0 p0
    1 ! p0
    -1
    1 0 -1
    0 p0
    1 ! p0
    -1

Since even state-based automata are stored as transition-based automata by Spot, it is also possible to force transition-based LBTT output to be used even if the automaton declares itself as state-based. This is done by passing `--lbtt=t`.

    ltl2tgba -B --lbtt=t 'GFp0'

    2 1t
    0 1
    0 0 -1 p0
    1 0 -1 ! p0
    -1
    1 0
    0 -1 p0
    1 -1 ! p0
    -1

Note that the LBTT output generalizes the format output by LBT with support for transition-based acceptance. Both formats however are restricted to atomic propositions of the form `p0`, `p1`, etc… In case other atomic propositions are used, Spot output them in double quotes. This second extension of the format was introduced by ltl2dstar.

    ltl2tgba -B --lbtt 'a U b'

    2 1
    0 1 -1
    1 "b"
    0 & "a" ! "b"
    -1
    1 0 0 -1
    1 t
    -1

## Spin output

Spin never claims can be requested using `-s` or `--spin`. They can only represent Büchi automata, so these options imply `--ba`.

    ltl2tgba -s 'a U b'

    never { /* a U b */
    T0_init:
      if
      :: (b) -> goto accept_all
      :: ((a) && (!(b))) -> goto T0_init
      fi;
    accept_all:
      skip
    }

Recent versions of Spin (starting with Spin 6.2.4) output never claims in a slightly different style that can be requested using either `-s6` or `--spin=6`:

    ltl2tgba -s6 'a U b'

    never { /* a U b */
    T0_init:
      do
      :: atomic { (b) -> assert(!(b)) }
      :: ((a) && (!(b))) -> goto T0_init
      od;
    accept_all:
      skip
    }

(Note that while Spot is able to read never claims that follow any of these two styles, it is not capable of interpreting an arbitrary piece of Promela syntax.)

## Dot output

The `-d` or `--dot` option causes automata to be output in GraphViz's format.

    ltl2tgba '(Ga -> Gb) W c' -d

    digraph "(Gb | F!a) W c" {
      rankdir=LR
      label="Inf(0)\n[Büchi]"
      labelloc="t"
      node [shape="circle"]
      I [label="", style=invis, width=0]
      I -> 0
      0 [label="0"]
      0 -> 0 [label="!a & !c\n{0}"]
      0 -> 1 [label="c"]
      0 -> 2 [label="a & !c"]
      0 -> 3 [label="a & b & !c"]
      1 [label="1"]
      1 -> 1 [label="1\n{0}"]
      2 [label="2"]
      2 -> 0 [label="!a & !c\n{0}"]
      2 -> 1 [label="!a & c"]
      2 -> 2 [label="a & !c"]
      2 -> 4 [label="a & c"]
      3 [label="3"]
      3 -> 3 [label="b\n{0}"]
      4 [label="4"]
      4 -> 1 [label="!a"]
      4 -> 4 [label="a"]
    }

### Converting dot output to images or pdf

This output should be processed with `dot` to be converted into a picture. For instance use `dot -Tpng` or `dot -Tpdf`. The pictures on this page are produced with `dot -Tsvg`.

    ltl2tgba '(Ga -> Gb) W c' -d | dot -Tsvg

In the documentation we display automata using SVG, but the actual steps used to obtain those SVG files are usually not relevant to the topics being discussed. So for simplicity we will usually omit the calls to `dot -Tsvg`, and will often also omit the use of the `-d` option.

### Customizing the dot output

This output can be customized by passing optional characters to the `--dot` option. For instance `v` requests a vertical layout (instead of the default horizontal layout), `c` requests circle states, `s` causes strongly-connected components to be displayed, `n` causes the name (see below) of the automaton to be displayed, and `a` causes the acceptance condition to be shown as well. Option `b` causes sets to be output as bullets (e.g., ⓿ instead of `{0}`); option `r` (for rainbow) causes sets to be displayed in different colors, while option `R` also uses colors, but it chooses them depending on whether a set is used with Fin-acceptance, Inf-acceptance, or both. Option `C(COLOR)` can be used to color all states using `COLOR`, and the option `f(FONT)` is used to select a font name: it is often necessary when `b` is used to ensure the characters ⓿, ❶, etc. are all selected from the same font.

    ltl2tgba --dot=vcsna '(Ga -> Gb) W c'

    digraph "(Gb | F!a) W c" {
      label="(Gb | F!a) W c\nInf(0)\n[Büchi]"
      labelloc="t"
      node [shape="circle"]
      I [label="", style=invis, height=0]
      I -> 0
      subgraph cluster_0 {
      color=green
      label=""
      1 [label="1"]
      }
      subgraph cluster_1 {
      color=red
      label=""
      4 [label="4"]
      }
      subgraph cluster_2 {
      color=green
      label=""
      3 [label="3"]
      }
      subgraph cluster_3 {
      color=green
      label=""
      0 [label="0"]
      2 [label="2"]
      }
      0 -> 0 [label="!a & !c\n{0}"]
      0 -> 1 [label="c"]
      0 -> 2 [label="a & !c"]
      0 -> 3 [label="a & b & !c"]
      1 -> 1 [label="1\n{0}"]
      2 -> 0 [label="!a & !c\n{0}"]
      2 -> 1 [label="!a & c"]
      2 -> 2 [label="a & !c"]
      2 -> 4 [label="a & c"]
      3 -> 3 [label="b\n{0}"]
      4 -> 1 [label="!a"]
      4 -> 4 [label="a"]
    }

The acceptance condition is displayed in the same way as in the HOA format. Here `Inf(0)` means that runs are accepting if and only if they visit some the transitions in the set #0 infinitely often. For well known acceptance conditions (as Büchi in this case), their name is also displayed in bracket below.

The strongly connected components are displayed using the following colors:

- green components contain an accepting cycle
- red components contain no accepting cycle
- black components are trivial (i.e., they contain no cycle)
- gray components are useless (i.e., they are non-accepting, and are only followed by non-accepting components)

Here is an example involving all colors:

The dot output can also be customized via two environment variables:

- `SPOT_DOTDEFAULT` contains default arguments for the `--dot` option (for when it is used implicitly, or used as just `--dot` without argument). For instance after `export SPOT_DOTDEFAULT=vcsn`, using `--dot` is equivalent to `--dot=vcsn`. However using `--dot=xyz` (for any value of `xyz`, even empty) will ignore the `SPOT_DOTDEFAULT` variable. If the argument of `--dot` contains a dot character, then this dot is replaced by the contents of `SPOT_DOTDEFAULT`. So `--dot=.A` would be equivalent to `--dot=vcsnA` with our example definition of `SPOT_DOTDEFAULT`.
- `SPOT_DOTEXTRA` may contains an arbitrary string that will be emitted in the dot output before the first state. This can be used to modify any attribute. For instance (except for this page, where we had do demonstrate the various options of `--dot`, and a few pages where we show the `--dot` output verbatim) all the automata displayed in this documentation are generated with the following environment variables set:

    export SPOT_DOTDEFAULT='Brf(Lato)C(#ffffa0)'
    export SPOT_DOTEXTRA='node[fontsize=12] fontsize=12 stylesheet="spot.css" edge[arrowhead=vee, arrowsize=.7, fontsize=12]'

### SVG and CSS

Each state, edge, or SCC in an automaton has a unique number. When passing option `i` to the dot printer, this unique number will be used to form a unique `id` attribute for these elements: a prefix `S` (for state), `E` (for edge), or "SCC=" is simply added to the unique number. Additionally, using `i(graphid)` will define `graphid` as that `id` of the automaton. GraphViz will keep these identifier in the generated SVG, so this makes it possible to modify rendering of the automaton using CSS or javascript.

As an example, the CSS file we use on this page contains:

    #iddemo #E3 path{animation:flashstroke 1s linear infinite;}
    @keyframes flashstroke{50%{stroke:red;stroke-width:1.5;}}
    #iddemo #E3 polygon{animation:flashfill 1s linear infinite;}
    @keyframes flashfill{50%{stroke:red;stroke-width:1.5;fill:red}}

therefore the third edge of any graph whose `id` is `iddemo` will be animated:

    ltl2tgba -G -D 'GFa <-> XGb' --dot='i(iddemo).'

### Working with `dot2tex`

The `dot2tex` program interacts with GraphViz to convert dot files into TeX figures. The layout is still done by tools provided by GraphViz (i.e. `dot`, `neato`, `circo`, …) but the actual rendering is done using LaTeX with the TikZ or PSTricks packages. One advantage is that this allows embedding math formulas into the graph, something GraphViz alone cannot do. Another advantage is that you can then easily edit the LaTeX figure, for instance to add additional graphical elements.

The `dot` formater of Spot has an option `x`, that is convenient to use with `dot2tex`. This option causes labels to be rendered as LaTeX mathematical formulas instead of ASCII text.

    ltl2tgba 'p0 U p1' --dot=x | dot2tex --autosize --nominsize > out.tex

The above command should give you a LaTeX file that compiles to the following figure:

Here is an example with bullets denoting acceptance sets, and SCCs:

    ltl2tgba -G -D '!a & FGa' --dot=sbarx | dot2tex --autosize --nominsize > out.tex

Caveats:

- `dot2tex` should be called with option `--autosize` in order to compute the size of each label before calling GraphViz to layout the graph. This is because GraphViz cannot compute the correct size of mathematical formulas. Make sure you use `dot2tex` version 2.11 or later, as earlier releases had a bug where sizes were interpreted as integers instead of floats, causing labels or shapes to disappear.
- The default size of nodes seems slightly too big for our usage. Using `--nominsize` is just one way around it. Refer to the `dot2tex` manual for finer ways to set the node size.

## Statistics

The `--stats` option takes a format string parameter to specify what and how statistics should be output.

Most tools support a common set of statistics about the output automaton (like `%s` for the number of states, `%t` for transitions, `%e` for edges, etc.). Additional statistics might be available depending on what the tool does (for instance `autfilt` also uses capitalized letters `%S`, `%T`, and `%E` to display the same statistics about the input automaton). All the available statistics are displayed when a tool is run with `--help`.

For instance here are the statistics available in `randaut`:

    %%                         a single %
    %a                         number of acceptance sets
    %c, %[LETTERS]c            number of SCCs; you may filter the SCCs to count
                               using the following LETTERS, possibly
                               concatenated: (a) accepting, (r) rejecting, (c)
                               complete, (v) trivial, (t) terminal, (w) weak,
                               (iw) inherently weak. Use uppercase letters to
                               negate them.
    %d                         1 if the output is deterministic, 0 otherwise
    %e, %[LETTER]e             number of edges (add one LETTER to select (r)
                               reachable [default], (u) unreachable, (a) all).
    %F                         seed number
    %g, %[LETTERS]g            acceptance condition (in HOA syntax); add brackets
                               to print an acceptance name instead and LETTERS to
                               tweak the format: (0) no parameters, (a)
                               accentuated, (b) abbreviated, (d) style used in
                               dot output, (g) no generalized parameter, (l)
                               recognize Street-like and Rabin-like, (m) no main
                               parameter, (p) no parity parameter, (o) name
                               unknown acceptance as 'other', (s) shorthand for
                               'lo0'.
    %h                         the automaton in HOA format on a single line (use
                               %[opt]h to specify additional options as in
                               --hoa=opt)
    %L                         automaton number
    %m                         name of the automaton
    %n                         number of nondeterministic states in output
    %p                         1 if the output is complete, 0 otherwise
    %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, %[LETTER]s             number of states (add one LETTER to select (r)
                               reachable [default], (u) unreachable, (a) all).
    %t, %[LETTER]t             number of transitions (add one LETTER to select
                               (r) reachable [default], (u) unreachable, (a)
                               all).
    %u, %[e]u                  number of states (or [e]dges) with universal
                               branching
    %u, %[LETTER]u             1 if the automaton contains some universal
                               branching (or a number of [s]tates or [e]dges with
                               universal branching)
    %w                         one word accepted by the output automaton
    %x, %[LETTERS]x            number of atomic propositions declared in the
                               automaton;  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

In most tools `%F` and `%L` are the input filename and line number, but as this makes no sense in `randaut`, these two sequences emit numbers related to the generation of automata.

For instance let's generate 1000 random automata with 100 states and density 0.2, and just count the number of edges in each automaton. Then use `R` to summarize the distribution of these values:

    randaut -e0.2 -Q100 -n1000 a --stats %e > size.csv
    Rscript -e "summary(read.csv('size.csv', header=FALSE, col.names='edges'))"

        edges
    Min.   :1939
    1st Qu.:2056
    Median :2083
    Mean   :2082
    3rd Qu.:2107
    Max.   :2233

For \(Q=100\) states and density \(D=0.2\) the expected degree of each state is \(1+(Q-1)D = 1+99\times 0.2 = 20.8\), so the expected number of edges should be \(20.8\times100=2080\).

## Timing

Two of the statistics are related to time: `%r` displays wall-clock time, while `%R` displays CPU-time.

    genltl --or-gf=1..8 | ltl2tgba --high --stats='%f,%r,%R'

    GFp1,0.000946222,0
    GF(p1 | p2),0.00138371,0
    GF(p1 | p2 | p3),0.003373,0
    GF(p1 | p2 | p3 | p4),0.000621515,0
    GF(p1 | p2 | p3 | p4 | p5),0.000586381,0
    GF(p1 | p2 | p3 | p4 | p5 | p6),0.000731476,0
    GF(p1 | p2 | p3 | p4 | p5 | p6 | p7),0.000614633,0
    GF(p1 | p2 | p3 | p4 | p5 | p6 | p7 | p8),0.000678737,0.01

Note that `%r` is implemented using the most precise clock available and usually has nanosecond precision, while `%R` uses the `times()` system call (when available) and is usually only precise up to 1/100 of a second. However, as a wall-clock time, `%r` will also be affected by the load of the machine: if a machine is overloaded, or swapping a lot, you may notice a wall-clock time that is significantly higher than the CPU time measured by `%R`.

Additional arguments may be passed to `%R` to select the time that must be output. By default, this the CPU-time spent in both user code and system calls. This can be restricted using one of `u` (user) or `s` (system). Also by default this includes the CPU-time for the current process and any of its children: adding `p` (parent) and `c` (children) will show only the selected time. Note that few tools actually execute other processes: `autfilt` and `ltl2tgba` can do so when calling a SAT solver for SAT-based minimization, and `ltldo` will obviously call any listed tool. However in the case of `ltldo` the measured time is that of executing the other tools, so the result of `%[p]R` is likely to be always 0.

Here is an example where we use `ltldo` to benchmark the (default) `--high` option of `ltl2tba` against the `--low` option, computing for each option the overall wall-clock time, CPU-time spent in `ltldo`, and CPU-time spent in `ltl2tgba`:

    genltl --or-gf=1..8 |
    ltldo '{high}ltl2tgba' '{low}ltl2tgba --low' --stats='%T,%f,%r,%[p]R,%[c]R'

    high,GFp1,0.0388069,0,0.05
    low,GFp1,0.0375546,0,0.04
    high,GFp1 | GFp2,0.0401419,0.01,0.04
    low,GFp1 | GFp2,0.0373387,0,0.05
    high,GFp1 | GFp2 | GFp3,0.0417641,0,0.05
    low,GFp1 | GFp2 | GFp3,0.0377401,0,0.04
    high,GFp1 | GFp2 | GFp3 | GFp4,0.0387336,0,0.05
    low,GFp1 | GFp2 | GFp3 | GFp4,0.038309,0,0.04
    high,GFp1 | GFp2 | GFp3 | GFp4 | GFp5,0.0395621,0,0.05
    low,GFp1 | GFp2 | GFp3 | GFp4 | GFp5,0.0385495,0,0.04
    high,GFp1 | GFp2 | GFp3 | GFp4 | GFp5 | GFp6,0.0387999,0,0.04
    low,GFp1 | GFp2 | GFp3 | GFp4 | GFp5 | GFp6,0.0384242,0,0.05
    high,GFp1 | GFp2 | GFp3 | GFp4 | GFp5 | GFp6 | GFp7,0.0388995,0,0.04
    low,GFp1 | GFp2 | GFp3 | GFp4 | GFp5 | GFp6 | GFp7,0.0389683,0,0.05
    high,GFp1 | GFp2 | GFp3 | GFp4 | GFp5 | GFp6 | GFp7 | GFp8,0.0392739,0,0.04
    low,GFp1 | GFp2 | GFp3 | GFp4 | GFp5 | GFp6 | GFp7 | GFp8,0.0382817,0,0.05

## Naming automata

Automata can be given names. This name can be output in the HOA format, but also in GraphViz output when `--dot=n` is given.

By default, `ltl2tgba` will use the input formula as name. Other tools have no default name. This name can be changed using the `--name` option, that takes a format string similar to the one of `--stats`.

    ltl2tgba --name='TGBA for %f' --dot=n 'a U b'

If you have an automaton saved in the HOA format, you can extract its name using `autfilt --stats=%M input.hoa`. The `%M` escape sequence is replaced by the name of the input automaton.

Here is a pipeline of commands that generates five LTL formulas \(\varphi\) such that both \(\varphi\) and \(\lnot\varphi\) are translated into a 3-state TGBA by `ltl2tgba`. It starts by generating an infinite stream of random LTL formulas using `a` and `b` as atomic propositions, then it converts these formulas as TGBA (in the HOA format, therefore carrying the formula as name), filtering only the TGBA with 3 states and outputting `!(%M)` (that is the negation of the associated formula), translating the resulting formulas as TGBA, again retaining only the names (i.e. formulas) of the automata with 3 states, and finally restricting the output to the first 5 matches using `autfilt -n5`.

    randltl -n -1 a b |
    ltl2tgba |
    autfilt --states=3 --stats='!(%M)' |
    ltl2tgba |
    autfilt --states=3 --stats=%M -n5

    G(b | F(b & Fa))
    (!a | b | (!b & (b W Ga))) & (a | (!b & (b | (!b M F!a))))
    (!a | (!a R b)) & (a | (a U !b))
    !a & F((!a | FG!a) & (a | GFa))
    X(!b W a)

Note that the above result can also be obtained without using `autfilt` and automata names. We can use the fact that `ltl2tgba --stats` can output the automaton size, and that `ltl2tgba` is also capable of reading from a CSV file (`-F-/2` instructs `ltl2tgba` to read the standard input as if it was a CSV file, and to process its second column):

    randltl -n -1 a b |                # generate a stream of random LTL formulas
    ltl2tgba -F- --stats='%s,!(%f)' |  # for each formula output "states,negated formula"
    grep '^3,' |                       # keep only formulas with 3 states
    ltl2tgba -F-/2 --stats='%s,%f' |   # for each negated formula output "states,formula"
    grep '^3,' |                       # keep only negated formulas with 3 states
    head -n5 | cut -d, -f2             # return the five first formulas

    G(b | F(b & Fa))
    (!a | b | (!b & (b W Ga))) & (a | (!b & (b | (!b M F!a))))
    (!a | (!a R b)) & (a | (a U !b))
    !a & F((!a | FG!a) & (a | GFa))
    X(!b W a)

Note that the `-F-` argument in the first call to `ltl2tgba` is superfluous as the tool default to reading from its standard input. But we put it there for symmetry with the second call.

## Naming output

By default, all output is sent to standard output, so you can either redirect it to a file, or pipe it to another program. You can also use the `--output` (a.k.a. `-o`) option to specify a filename where automata should be written. The advantage over a shell redirection, is that you may build a name using the same escape sequences as used by `--stats` and `--name`.

For instance `%d` is replaced by 0 or 1 depending on whether the automaton is deterministic. We can generate 20 random automata, and output them in two files depending on their determinism:

    randaut -n 20 -Q2 -e1 1 -o out-det%d.hoa
    autfilt -c out-det0.hoa    # Count of non-deterministic automata
    autfilt -c out-det1.hoa    # Count of deterministic automata

    14
    6

If you use this feature, beware that the output filename is only truncated once a first automaton is output to it: so if no automaton is output for a given filename, the existing file will be left untouched. For instance if we run the above commands again, but forcing `randaut` to output 20 deterministic automata, it may look like we produced more than 20 automata:

    randaut -D -n 20 -Q2 -e1 1 -o out-det%d.hoa
    autfilt -c out-det0.hoa    # Count of non-deterministic automata
    autfilt -c out-det1.hoa    # Count of deterministic automata

    14
    20

This is because the `out-det0.hoa` file hasn't changed from the previous execution, while `out-det1.hoa` has been overwritten.

In the case where you want to append to a file instead of overwriting it, prefix the output filename with `>>` as in

    randaut -D -n 20 -Q2 1 -o '>>out-det%d.hoa'

(You need the quotes so that the shell does not interpret `>>`.)