mirror of
https://github.com/torvalds/linux.git
synced 2024-12-28 22:02:28 +00:00
Documentation/rv: Add deterministic automaton documentation
Add documentation about deterministic automaton and its possible representations (formal, graphic, .dot and C). Link: https://lkml.kernel.org/r/387edaed87630bd5eb37c4275045dfd229700aa6.1659052063.git.bristot@kernel.org Cc: Wim Van Sebroeck <wim@linux-watchdog.org> Cc: Guenter Roeck <linux@roeck-us.net> Cc: Jonathan Corbet <corbet@lwn.net> Cc: Ingo Molnar <mingo@redhat.com> Cc: Thomas Gleixner <tglx@linutronix.de> Cc: Peter Zijlstra <peterz@infradead.org> Cc: Will Deacon <will@kernel.org> Cc: Catalin Marinas <catalin.marinas@arm.com> Cc: Marco Elver <elver@google.com> Cc: Dmitry Vyukov <dvyukov@google.com> Cc: "Paul E. McKenney" <paulmck@kernel.org> Cc: Shuah Khan <skhan@linuxfoundation.org> Cc: Gabriele Paoloni <gpaoloni@redhat.com> Cc: Juri Lelli <juri.lelli@redhat.com> Cc: Clark Williams <williams@redhat.com> Cc: Tao Zhou <tao.zhou@linux.dev> Cc: Randy Dunlap <rdunlap@infradead.org> Cc: linux-doc@vger.kernel.org Cc: linux-kernel@vger.kernel.org Cc: linux-trace-devel@vger.kernel.org Signed-off-by: Daniel Bristot de Oliveira <bristot@kernel.org> Signed-off-by: Steven Rostedt (Google) <rostedt@goodmis.org>
This commit is contained in:
Daniel Bristot de Oliveira
Steven Rostedt (Google)
parent
e3c9fc78f0
commit
4041b9bbfb
184
Documentation/trace/rv/deterministic_automata.rst
Normal file
184
Documentation/trace/rv/deterministic_automata.rst
Normal file
@ -0,0 +1,184 @@
|
||||
Deterministic Automata
|
||||
======================
|
||||
|
||||
Formally, a deterministic automaton, denoted by G, is defined as a quintuple:
|
||||
|
||||
*G* = { *X*, *E*, *f*, x\ :subscript:`0`, X\ :subscript:`m` }
|
||||
|
||||
where:
|
||||
|
||||
- *X* is the set of states;
|
||||
- *E* is the finite set of events;
|
||||
- x\ :subscript:`0` is the initial state;
|
||||
- X\ :subscript:`m` (subset of *X*) is the set of marked (or final) states.
|
||||
- *f* : *X* x *E* -> *X* $ is the transition function. It defines the state
|
||||
transition in the occurrence of an event from *E* in the state *X*. In the
|
||||
special case of deterministic automata, the occurrence of the event in *E*
|
||||
in a state in *X* has a deterministic next state from *X*.
|
||||
|
||||
For example, a given automaton named 'wip' (wakeup in preemptive) can
|
||||
be defined as:
|
||||
|
||||
- *X* = { ``preemptive``, ``non_preemptive``}
|
||||
- *E* = { ``preempt_enable``, ``preempt_disable``, ``sched_waking``}
|
||||
- x\ :subscript:`0` = ``preemptive``
|
||||
- X\ :subscript:`m` = {``preemptive``}
|
||||
- *f* =
|
||||
- *f*\ (``preemptive``, ``preempt_disable``) = ``non_preemptive``
|
||||
- *f*\ (``non_preemptive``, ``sched_waking``) = ``non_preemptive``
|
||||
- *f*\ (``non_preemptive``, ``preempt_enable``) = ``preemptive``
|
||||
|
||||
One of the benefits of this formal definition is that it can be presented
|
||||
in multiple formats. For example, using a *graphical representation*, using
|
||||
vertices (nodes) and edges, which is very intuitive for *operating system*
|
||||
practitioners, without any loss.
|
||||
|
||||
The previous 'wip' automaton can also be represented as::
|
||||
|
||||
preempt_enable
|
||||
+---------------------------------+
|
||||
v |
|
||||
#============# preempt_disable +------------------+
|
||||
--> H preemptive H -----------------> | non_preemptive |
|
||||
#============# +------------------+
|
||||
^ |
|
||||
| sched_waking |
|
||||
+--------------+
|
||||
|
||||
Deterministic Automaton in C
|
||||
----------------------------
|
||||
|
||||
In the paper "Efficient formal verification for the Linux kernel",
|
||||
the authors present a simple way to represent an automaton in C that can
|
||||
be used as regular code in the Linux kernel.
|
||||
|
||||
For example, the 'wip' automata can be presented as (augmented with comments)::
|
||||
|
||||
/* enum representation of X (set of states) to be used as index */
|
||||
enum states {
|
||||
preemptive = 0,
|
||||
non_preemptive,
|
||||
state_max
|
||||
};
|
||||
|
||||
#define INVALID_STATE state_max
|
||||
|
||||
/* enum representation of E (set of events) to be used as index */
|
||||
enum events {
|
||||
preempt_disable = 0,
|
||||
preempt_enable,
|
||||
sched_waking,
|
||||
event_max
|
||||
};
|
||||
|
||||
struct automaton {
|
||||
char *state_names[state_max]; // X: the set of states
|
||||
char *event_names[event_max]; // E: the finite set of events
|
||||
unsigned char function[state_max][event_max]; // f: transition function
|
||||
unsigned char initial_state; // x_0: the initial state
|
||||
bool final_states[state_max]; // X_m: the set of marked states
|
||||
};
|
||||
|
||||
struct automaton aut = {
|
||||
.state_names = {
|
||||
"preemptive",
|
||||
"non_preemptive"
|
||||
},
|
||||
.event_names = {
|
||||
"preempt_disable",
|
||||
"preempt_enable",
|
||||
"sched_waking"
|
||||
},
|
||||
.function = {
|
||||
{ non_preemptive, INVALID_STATE, INVALID_STATE },
|
||||
{ INVALID_STATE, preemptive, non_preemptive },
|
||||
},
|
||||
.initial_state = preemptive,
|
||||
.final_states = { 1, 0 },
|
||||
};
|
||||
|
||||
The *transition function* is represented as a matrix of states (lines) and
|
||||
events (columns), and so the function *f* : *X* x *E* -> *X* can be solved
|
||||
in O(1). For example::
|
||||
|
||||
next_state = automaton_wip.function[curr_state][event];
|
||||
|
||||
Graphviz .dot format
|
||||
--------------------
|
||||
|
||||
The Graphviz open-source tool can produce the graphical representation
|
||||
of an automaton using the (textual) DOT language as the source code.
|
||||
The DOT format is widely used and can be converted to many other formats.
|
||||
|
||||
For example, this is the 'wip' model in DOT::
|
||||
|
||||
digraph state_automaton {
|
||||
{node [shape = circle] "non_preemptive"};
|
||||
{node [shape = plaintext, style=invis, label=""] "__init_preemptive"};
|
||||
{node [shape = doublecircle] "preemptive"};
|
||||
{node [shape = circle] "preemptive"};
|
||||
"__init_preemptive" -> "preemptive";
|
||||
"non_preemptive" [label = "non_preemptive"];
|
||||
"non_preemptive" -> "non_preemptive" [ label = "sched_waking" ];
|
||||
"non_preemptive" -> "preemptive" [ label = "preempt_enable" ];
|
||||
"preemptive" [label = "preemptive"];
|
||||
"preemptive" -> "non_preemptive" [ label = "preempt_disable" ];
|
||||
{ rank = min ;
|
||||
"__init_preemptive";
|
||||
"preemptive";
|
||||
}
|
||||
}
|
||||
|
||||
This DOT format can be transformed into a bitmap or vectorial image
|
||||
using the dot utility, or into an ASCII art using graph-easy. For
|
||||
instance::
|
||||
|
||||
$ dot -Tsvg -o wip.svg wip.dot
|
||||
$ graph-easy wip.dot > wip.txt
|
||||
|
||||
dot2c
|
||||
-----
|
||||
|
||||
dot2c is a utility that can parse a .dot file containing an automaton as
|
||||
in the example above and automatically convert it to the C representation
|
||||
presented in [3].
|
||||
|
||||
For example, having the previous 'wip' model into a file named 'wip.dot',
|
||||
the following command will transform the .dot file into the C
|
||||
representation (previously shown) in the 'wip.h' file::
|
||||
|
||||
$ dot2c wip.dot > wip.h
|
||||
|
||||
The 'wip.h' content is the code sample in section 'Deterministic Automaton
|
||||
in C'.
|
||||
|
||||
Remarks
|
||||
-------
|
||||
|
||||
The automata formalism allows modeling discrete event systems (DES) in
|
||||
multiple formats, suitable for different applications/users.
|
||||
|
||||
For example, the formal description using set theory is better suitable
|
||||
for automata operations, while the graphical format for human interpretation;
|
||||
and computer languages for machine execution.
|
||||
|
||||
References
|
||||
----------
|
||||
|
||||
Many textbooks cover automata formalism. For a brief introduction see::
|
||||
|
||||
O'Regan, Gerard. Concise guide to software engineering. Springer,
|
||||
Cham, 2017.
|
||||
|
||||
For a detailed description, including operations, and application on Discrete
|
||||
Event Systems (DES), see::
|
||||
|
||||
Cassandras, Christos G., and Stephane Lafortune, eds. Introduction to discrete
|
||||
event systems. Boston, MA: Springer US, 2008.
|
||||
|
||||
For the C representation in kernel, see::
|
||||
|
||||
De Oliveira, Daniel Bristot; Cucinotta, Tommaso; De Oliveira, Romulo
|
||||
Silva. Efficient formal verification for the Linux kernel. In:
|
||||
International Conference on Software Engineering and Formal Methods.
|
||||
Springer, Cham, 2019. p. 315-332.
|
||||
@ -7,3 +7,4 @@ Runtime Verification
|
||||
:glob:
|
||||
|
||||
runtime-verification.rst
|
||||
deterministic_automata.rst
|
||||
|
||||
@ -4,6 +4,9 @@
|
||||
# Copyright (C) 2019-2022 Red Hat, Inc. Daniel Bristot de Oliveira <bristot@kernel.org>
|
||||
#
|
||||
# Automata object: parse an automata in dot file digraph format into a python object
|
||||
#
|
||||
# For further information, see:
|
||||
# Documentation/trace/rv/deterministic_automata.rst
|
||||
|
||||
import ntpath
|
||||
|
||||
|
||||
@ -9,6 +9,9 @@
|
||||
# de Oliveira, D. B. and Cucinotta, T. and de Oliveira, R. S.
|
||||
# "Efficient Formal Verification for the Linux Kernel." International
|
||||
# Conference on Software Engineering and Formal Methods. Springer, Cham, 2019.
|
||||
#
|
||||
# For further information, see:
|
||||
# Documentation/trace/rv/deterministic_automata.rst
|
||||
|
||||
if __name__ == '__main__':
|
||||
from dot2 import dot2c
|
||||
|
||||
@ -9,6 +9,9 @@
|
||||
# de Oliveira, D. B. and Cucinotta, T. and de Oliveira, R. S.
|
||||
# "Efficient Formal Verification for the Linux Kernel." International
|
||||
# Conference on Software Engineering and Formal Methods. Springer, Cham, 2019.
|
||||
#
|
||||
# For further information, see:
|
||||
# Documentation/trace/rv/deterministic_automata.rst
|
||||
|
||||
from dot2.automata import Automata
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user