Documentation/rv: Add documentation for linear temporal logic monitors

   runtime-verification.rst

   deterministic_automata.rst

   linear_temporal_logic.rst

   monitor_synthesis.rst

   da_monitor_instrumentation.rst

   monitor_wip.rst

Linear temporal logic

=====================

Introduction

------------

Runtime verification monitor is a verification technique which checks that the

kernel follows a specification. It does so by using tracepoints to monitor the

kernel's execution trace, and verifying that the execution trace sastifies the

specification.

Initially, the specification can only be written in the form of deterministic

automaton (DA).  However, while attempting to implement DA monitors for some

complex specifications, deterministic automaton is found to be inappropriate as

the specification language. The automaton is complicated, hard to understand,

and error-prone.

Thus, RV monitors based on linear temporal logic (LTL) are introduced. This type

of monitor uses LTL as specification instead of DA. For some cases, writing the

specification as LTL is more concise and intuitive.

Many materials explain LTL in details. One book is::

  Christel Baier and Joost-Pieter Katoen: Principles of Model Checking, The MIT

  Press, 2008.

Grammar

-------

Unlike some existing syntax, kernel's implementation of LTL is more verbose.

This is motivated by considering that the people who read the LTL specifications

may not be well-versed in LTL.

Grammar:

    ltl ::= opd | ( ltl ) | ltl binop ltl | unop ltl

Operands (opd):

    true, false, user-defined names consisting of upper-case characters, digits,

    and underscore.

Unary Operators (unop):

    always

    eventually

    not

Binary Operators (binop):

    until

    and

    or

    imply

    equivalent

This grammar is ambiguous: operator precedence is not defined. Parentheses must

be used.

Example linear temporal logic

-----------------------------

.. code-block::

   RAIN imply (GO_OUTSIDE imply HAVE_UMBRELLA)

means: if it is raining, going outside means having an umbrella.

.. code-block::

   RAIN imply (WET until not RAIN)

means: if it is raining, it is going to be wet until the rain stops.

.. code-block::

   RAIN imply eventually not RAIN

means: if it is raining, rain will eventually stop.

The above examples are referring to the current time instance only. For kernel

verification, the `always` operator is usually desirable, to specify that

something is always true at the present and for all future. For example::

    always (RAIN imply eventually not RAIN)

means: *all* rain eventually stops.

In the above examples, `RAIN`, `GO_OUTSIDE`, `HAVE_UMBRELLA` and `WET` are the

"atomic propositions".

Monitor synthesis

-----------------

To synthesize an LTL into a kernel monitor, the `rvgen` tool can be used:

`tools/verification/rvgen`. The specification needs to be provided as a file,

and it must have a "RULE = LTL" assignment. For example::

    RULE = always (ACQUIRE imply ((not KILLED and not CRASHED) until RELEASE))

which says: if `ACQUIRE`, then `RELEASE` must happen before `KILLED` or

`CRASHED`.

The LTL can be broken down using sub-expressions. The above is equivalent to:

   .. code-block::

    RULE = always (ACQUIRE imply (ALIVE until RELEASE))

    ALIVE = not KILLED and not CRASHED

From this specification, `rvgen` generates the C implementation of a Buchi

automaton - a non-deterministic state machine which checks the satisfiability of

the LTL. See Documentation/trace/rv/monitor_synthesis.rst for details on using

`rvgen`.

References

----------

One book covering model checking and linear temporal logic is::

  Christel Baier and Joost-Pieter Katoen: Principles of Model Checking, The MIT

  Press, 2008.

For an example of using linear temporal logic in software testing, see::

  Ruijie Meng, Zhen Dong, Jialin Li, Ivan Beschastnikh, and Abhik Roychoudhury.

  2022. Linear-time temporal logic guided greybox fuzzing. In Proceedings of the

  44th International Conference on Software Engineering (ICSE '22).  Association

  for Computing Machinery, New York, NY, USA, 1343–1355.

  https://doi.org/10.1145/3510003.3510082

The kernel's LTL monitor implementation is based on::

  Gerth, R., Peled, D., Vardi, M.Y., Wolper, P. (1996). Simple On-the-fly

  Automatic Verification of Linear Temporal Logic. In: Dembiński, P., Średniawa,

  M. (eds) Protocol Specification, Testing and Verification XV. PSTV 1995. IFIP

  Advances in Information and Communication Technology. Springer, Boston, MA.

  https://doi.org/10.1007/978-0-387-34892-6_1

RV monitor synthesis

--------------------

The synthesis of automata-based models into the Linux *RV monitor* abstraction

is automated by the rvgen tool and the rv/da_monitor.h header file that

contains a set of macros that automatically generate the monitor's code.

The synthesis of a specification into the Linux *RV monitor* abstraction is

automated by the rvgen tool and the header file containing common code for

creating monitors. The header files are:

  * rv/da_monitor.h for deterministic automaton monitor.

  * rv/ltl_monitor.h for linear temporal logic monitor.

rvgen

-----

The rvgen utility leverages dot2c by converting an automaton model in

the DOT format into the C representation [1] and creating the skeleton of

a kernel monitor in C.

The rvgen utility converts a specification into the C presentation and creating

the skeleton of a kernel monitor in C.

For example, it is possible to transform the wip.dot model present in

[1] into a per-cpu monitor with the following command::

The wip.c file contains the monitor declaration and the starting point for

the system instrumentation.

Monitor macros

--------------

Similarly, a linear temporal logic monitor can be generated with the following

command::

  $ rvgen monitor -c ltl -s pagefault.ltl -t per_task

This generates pagefault/ directory with:

- pagefault.h: The Buchi automaton (the non-deterministic state machine to

  verify the specification)

- pagefault.c: The skeleton for the RV monitor

Monitor header files

--------------------

The header files:

- `rv/da_monitor.h` for deterministic automaton monitor

- `rv/ltl_monitor` for linear temporal logic monitor

include common macros and static functions for implementing *Monitor

Instance(s)*.

The rv/da_monitor.h enables automatic code generation for the *Monitor

Instance(s)* using C macros.

The benefits of having all common functionalities in a single header file are

3-fold:

The benefits of the usage of macro for monitor synthesis are 3-fold as it:

  - Reduce the code duplication;

  - Facilitate the bug fix/improvement;

  - Avoid the case of developers changing the core of the monitor code to

    manipulate the model in a (let's say) non-standard way.

- Reduces the code duplication;

- Facilitates the bug fix/improvement;

- Avoids the case of developers changing the core of the monitor code

  to manipulate the model in a (let's say) non-standard way.

rv/da_monitor.h

+++++++++++++++

This initial implementation presents three different types of monitor instances:

To notify the monitor that the system will be returning to the initial state,

so the system and the monitor should be in sync.

rv/ltl_monitor.h

++++++++++++++++

This file must be combined with the $(MODEL_NAME).h file (generated by `rvgen`)

to be complete. For example, for the `pagefault` monitor, the `pagefault.c`

source file must include::

  #include "pagefault.h"

  #include <rv/ltl_monitor.h>

(the skeleton monitor file generated by `rvgen` already does this).

`$(MODEL_NAME).h` (`pagefault.h` in the above example) includes the

implementation of the Buchi automaton - a non-deterministic state machine that

verifies the LTL specification. While `rv/ltl_monitor.h` includes the common

helper functions to interact with the Buchi automaton and to implement an RV

monitor. An important definition in `$(MODEL_NAME).h` is::

  enum ltl_atom {

      LTL_$(FIRST_ATOMIC_PROPOSITION),

      LTL_$(SECOND_ATOMIC_PROPOSITION),

      ...

      LTL_NUM_ATOM

  };

which is the list of atomic propositions present in the LTL specification

(prefixed with "LTL\_" to avoid name collision). This `enum` is passed to the

functions interacting with the Buchi automaton.

While generating code, `rvgen` cannot understand the meaning of the atomic

propositions. Thus, that task is left for manual work. The recommended pratice

is adding tracepoints to places where the atomic propositions change; and in the

tracepoints' handlers: the Buchi automaton is executed using::

  void ltl_atom_update(struct task_struct *task, enum ltl_atom atom, bool value)

which tells the Buchi automaton that the atomic proposition `atom` is now

`value`. The Buchi automaton checks whether the LTL specification is still

satisfied, and invokes the monitor's error tracepoint and the reactor if

violation is detected.

Tracepoints and `ltl_atom_update()` should be used whenever possible. However,

it is sometimes not the most convenient. For some atomic propositions which are

changed in multiple places in the kernel, it is cumbersome to trace all those

places. Furthermore, it may not be important that the atomic propositions are

updated at precise times. For example, considering the following linear temporal

logic::

  RULE = always (RT imply not PAGEFAULT)

This LTL states that a real-time task does not raise page faults. For this

specification, it is not important when `RT` changes, as long as it has the

correct value when `PAGEFAULT` is true.  Motivated by this case, another

function is introduced::

  void ltl_atom_fetch(struct task_struct *task, struct ltl_monitor *mon)

This function is called whenever the Buchi automaton is triggered. Therefore, it

can be manually implemented to "fetch" `RT`::

  void ltl_atom_fetch(struct task_struct *task, struct ltl_monitor *mon)

  {

      ltl_atom_set(mon, LTL_RT, rt_task(task));

  }

Effectively, whenever `PAGEFAULT` is updated with a call to `ltl_atom_update()`,

`RT` is also fetched. Thus, the LTL specification can be verified without

tracing `RT` everywhere.

For atomic propositions which act like events, they usually need to be set (or

cleared) and then immediately cleared (or set). A convenient function is

provided::

  void ltl_atom_pulse(struct task_struct *task, enum ltl_atom atom, bool value)

which is equivalent to::

  ltl_atom_update(task, atom, value);

  ltl_atom_update(task, atom, !value);

To initialize the atomic propositions, the following function must be

implemented::

  ltl_atoms_init(struct task_struct *task, struct ltl_monitor *mon, bool task_creation)

This function is called for all running tasks when the monitor is enabled. It is

also called for new tasks created after the enabling the monitor. It should

initialize as many atomic propositions as possible, for example::

  void ltl_atom_init(struct task_struct *task, struct ltl_monitor *mon, bool task_creation)

  {

      ltl_atom_set(mon, LTL_RT, rt_task(task));

      if (task_creation)

          ltl_atom_set(mon, LTL_PAGEFAULT, false);

  }

Atomic propositions not initialized by `ltl_atom_init()` will stay in the

unknown state until relevant tracepoints are hit, which can take some time. As

monitoring for a task cannot be done until all atomic propositions is known for

the task, the monitor may need some time to start validating tasks which have

been running before the monitor is enabled. Therefore, it is recommended to

start the tasks of interest after enabling the monitor.

Final remarks

-------------

With the monitor synthesis in place using the rv/da_monitor.h and

With the monitor synthesis in place using the header files and

rvgen, the developer's work should be limited to the instrumentation

of the system, increasing the confidence in the overall approach.