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# Kofola: modular complementation and inclusion checking for omega automata | ||
# Kofola: Modular Complementation and Inclusion Checking for Omega Automata | ||
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Kofola has been built on top of [SPOT](https://spot.lrde.epita.fr/) and | ||
Kofola is an open source tool for an efficient complementation and inclusion checking | ||
of automata over infinite words (omega automata). Kofola has been built on top of [SPOT](https://spot.lrde.epita.fr/) and | ||
inspired by [Seminator](https://github.com/mklokocka/seminator) and | ||
[COLA](https://github.com/liyong31/COLA). | ||
[COLA](https://github.com/liyong31/COLA). | ||
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### Requirements | ||
### Requirements and dependencies | ||
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For a successful build of Kofola, `cmake` of version 3.16 (or higher) together with a C++ compiler with a support of C++-17 standard is required. Additional requirements | ||
include: | ||
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* [Spot](https://spot.lrde.epita.fr/) | ||
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For Debian-like systems, Spot can be installed using the package `libspot-dev`. | ||
For building Spot from sources, download the recent version and run: | ||
``` | ||
./configure --enable-max-accsets=128 | ||
./configure | ||
``` | ||
One can set the maximal number of colors for an automaton when configuring Spot with --enable-max-accsets=INT | ||
One can set the maximal number of colors for an automaton when configuring Spot with `--enable-max-accsets=INT`. | ||
``` | ||
make && make install | ||
make | ||
sudo make install | ||
``` | ||
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### Compilation | ||
### Building Kofola | ||
Please run the following steps to compile Kofola after cloning this repo: | ||
``` | ||
mkdir build && cd build | ||
cmake .. | ||
cmake -DCMAKE_BUILD_TYPE=Release .. | ||
make | ||
``` | ||
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Then you will get an executable in `build/src/kofola`. | ||
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To use `kofola` for HyperLTL model checking, an example of execution is as follows (assuming we are in `build` directory): | ||
``` | ||
./src/kofola --hyperltl_mc ../hyperltl_ex/bp/concur_p1_1bit.hoa ../hyperltl_ex/bp/gni.hq | ||
``` | ||
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To use `kofola` for inclusion checking, an example of execution is as follows (assuming we are in `build` directory): | ||
``` | ||
./src/kofola --inclusion ../inclusion_ex/bakery_3procs_bakery_formula_S2_3proc_A.hoa ../inclusion_ex/bakery_3procs_bakery_formula_S2_3proc_B.hoa | ||
``` | ||
Then you will get an executable in `build/src/kofola`. Alternatively you can | ||
run `make release` in the root directory. | ||
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### HyperLTL MC input formats | ||
#### System | ||
As input format for system behavior, we decided to use the HOA format so that it can | ||
be easily parsed and stored by Spot as a Kripke structure. An example: | ||
``` | ||
HOA: v1 | ||
States: 4 | ||
Start: 3 | ||
AP: 3 "h_0" "l_0" "o_0" | ||
acc-name: all | ||
Acceptance: 0 t | ||
properties: state-labels explicit-labels state-acc deterministic | ||
--BODY-- | ||
State: [!0&!1&!2] 2 | ||
3 | ||
State: [!0&!1&!2] 3 | ||
4 | ||
State: [2&!0&!1] 4 | ||
5 | ||
State: [2&!0&!1] 5 | ||
2 | ||
--END-- | ||
``` | ||
#### Formula | ||
For LTL body of the HyperLTL formula we support the exact format that `Spot` supports. However, each atomic proposition (AP) | ||
is of the format `{ap_sys}_{trace_var}` with `ap_sys` standing for the atomic proposition used within the system and | ||
`trace_var` stands for the quantified trace. The `f` formula with quantifiers is then generated by the following syntax: | ||
``` | ||
f ::= ((forall trace_var.)* (exists trace_var.)*)* LTL | ||
trace_var ::= string | ||
``` | ||
An example of a property for the above system: | ||
``` | ||
forall A. forall B. exists C. (G ("{h_0}_{A}" <-> "{h_0}_{C}")) & (G("{l_0}_{B}" <-> "{l_0}_{C}")) | ||
``` |