# lps2pbes¶

The tool lps2pbes reads a modal formula as well as a linear process and generates a parameterised boolean equation system (PBES) of which the solution of the initial variable indicates whether the formula is valid in the initial state of the transition system. The generated PBES can be solved using tools such as pbes2bool, pbessolve or pbespgsolve.

When using particular formulas, for instance such as:

[true*]<a.b.c.d.e.f.g.h>true


then the standard translation to PBESs can yield a very PBES which is very elaborate to generate and can become large. This is due to the fact that the subformula <a.b.c.d.e.f.g.h> is translated into one PBES equation with a huge right hand side. This right hand side essentially reflects for any state of the linear process whether a trace a.b.c.d.e.f.g.h is possible. When using the flag --preprocess-modal-operators the formula is first transformed into the equivalent formula:

[true*]mu X1.<a>mu X2.<b>mu X3.<c>mu X4.<d>mu X5.<d>mu X6.<e>mu X7.<f>mu X8.<g>mu X9.<h>true


This formula replaces the single very large equation by 9 ones, where the right hand sides only contain the information whether a single action can be done. This is generally faster and yields a substantially smaller PBES. Note that elaborate generations of PBESs can already occur when using subformulas of the shape [a.b]... or <a.b>....

The tool pbessolve is capable of generating a counter example in the form of labelled transition systems, provided the PBES is generated using lps2pbes (or lts2pbes) using the --counter-example flag. The generated PBES is more complicated and may be harder to solve. Yet, these counter examples are very helpful in determining whether formulas do not hold. If formulas are valid, this flag can also be used to determine witnesses, i.e., evidence when formulas are valid. The tool pbes2bool can generate counter examples without the use of this flag. These counter-examples are solely based on the provided PBES and they must be manually be related to the original transition system.

Note that there is also an option --structured which can be used to generate boolean equation systems that do not contain both the conjunction and the disjunction operators among PBES variables in the right hand side. This flag can lead to a substantially larger number of equation (but linear in the original formula).

## Manual page for lps2pbes¶

### Usage¶

lps2pbes   [OPTION]... --formula=FILE [INFILE [OUTFILE]]


### Description¶

Convert the state formula in FILE and the LPS in INFILE to a parameterised boolean equation system (PBES) and save it to OUTFILE. If OUTFILE is not present, stdout is used. If INFILE is not present, stdin is used.

### Command line options¶

-c , --counter-example

add counter example equations to the generated PBES

-fFILE , --formulaFILE

use the state formula from FILE

-oFORMAT , --outFORMAT

use output format FORMAT:

bes

BES in internal format

pbes

PBES in internal format

pgsolver

BES in PGSolver format

text

PBES in textual (mCRL2) format

-m , --preprocess-modal-operators

insert dummy fixpoints in modal operators, which may lead to smaller PBESs

-s , --structured

generate equations such that no mixed conjunctions and disjunctions occur

-t , --timed

use the timed version of the algorithm, even for untimed LPS’s

--timings[FILE]

append timing measurements to FILE. Measurements are written to standard error if no FILE is provided

-u , --unoptimized

do not simplify boolean expressions

#### Standard options¶

-q , --quiet

do not display warning messages

-v , --verbose

display short intermediate messages

-d , --debug

display detailed intermediate messages

--log-levelLEVEL

display intermediate messages up to and including level

-h , --help

display help information

--version

display version information

### Author¶

Wieger Wesselink; Tim Willemse