# lpsrealelm¶

The tool replaces parameters of sort real from the linear process specification by parameters of sort Comp, which is an structured sort with three constants smaller, equal and larger. They represent that certain pairs of real expressions must be smaller, equal or larger to each other. If the resulting linear process does not contain MAY-actions, it is strongly bisimilar to the input lps. Otherwise, the result is may-bisimilar to the original.

## Example¶

Consider an LPS with the following process equation.

act  step, urgent, reset;
proc P(x:Real) = sum y:Real.(x<y)->step.P(y)
+ sum y:Real.(x<y && x<2)->urgent.P(y)
+ reset.P(0);

init P(0);


The tool transforms this to the following strongly bisimilar LPS (where it must be noted that in this particular case the condition x>=0 has been added to each summand in the input LPS).

sort Comp = struct smaller?is_smaller | equal?is_equal | larger?is_larger;

act  step,urgent,reset;

proc P(xi,xi00: Comp) =
!is_smaller(xi) ->
reset .
P(equal, smaller)
+ (is_smaller(xi00) && !is_smaller(xi)) ->
urgent .
P(larger, equal)
+ (!is_smaller(xi) && is_smaller(xi00)) ->
urgent .
P(larger, smaller)
+ (is_smaller(xi00) && !is_smaller(xi)) ->
urgent .
P(larger, larger)
+ (is_smaller(xi00) && !is_smaller(xi)) ->
step .
P(larger, equal)
+ (!is_smaller(xi) && is_smaller(xi00)) ->
step .
P(larger, smaller)
+ !is_smaller(xi) ->
step .
P(larger, larger);

init P(equal, smaller);


## Manual page for lpsrealelm¶

### Usage¶

lpsrealelm   [OPTION]... [INFILE [OUTFILE]]


### Description¶

Remove Real numbers from the linear process specification (LPS) in INFILE and write the result to OUTFILE. If INFILE is not present, stdin is used.

### Command line options¶

--max=NUM

perform at most NUM iterations

-QNUM , --qlimit=NUM

limit enumeration of quantifiers to NUM iterations. (Default NUM=1000, NUM=0 for unlimited).

-rNAME , --rewriter=NAME

use rewrite strategy NAME:

jitty

jitty rewriting

jittyc

compiled jitty rewriting

jittyp

jitty rewriting with prover

--timings[=FILE]

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

#### Standard options¶

-q , --quiet

do not display warning messages

-v , --verbose

display short intermediate messages

-d , --debug

display detailed intermediate messages

--log-level=LEVEL

display intermediate messages up to and including level

-h , --help

display help information

--version

display version information

--help-all

display help information, including hidden and experimental options

### Author¶

Jan Friso Groote and Jeroen Keiren