FSMs are needed¶
Finit State Machines (FSMs) are great to model behaviour and control flow. Probably it is one of the most used design patterns; some developers are not even aware they are using it (when using the State pattern). And non of the well-known system-programming-languages does support it directly – it’s a shame;-)
This leads to sub-optimal, often hard to maintain code. In Castle, you can use define a FSM directly. Let’s see why that is essential.
FSMs, an intro¶
The well known State pattern is basically an FSM. It has a finit (!) number of states, inputs (often
called events) and rules; the latter define the next state, which only depend on the current state and the
current input. Optionally, but typically for software: there are also actions: code that is executed on a
state-transition or the entry/exit of a state.
With a FSM one can model simple “automata”. It does not have real
memory –it does not remember how it gets in a state– but does act depending on this internal state. Therefore a FSM
can act differently on a second button-push: With the first push it goes to a state as <pressed-once>, and with the
second one to <pressed-twice>. And we can even define a states as <pressed-three-times,
<pressed-four-times, etc; but (a given) FSM has always a limited number of states.
As soon we add variable (eg counter) to the code; it’s no longer a FSM!
Conceptually coding a FSM is simple; but in practise it is troublesome to make it solid and maintainable. Typically
the result is a lot of code. Even a trivial FSM with only 3 states, 3 events, and a single function-call on
all possible transactions (but no entry/leave actions) will give about 30 lines. See the UML-diagram and (python) code
examples in the side-bar, for a first impression.
This straightforward implementation used a nested switch: for every \(S\) states we divert for every \(E\)
events; where we need 2 lines: one to update the state and one function-call. This leads to \(2*S*E\) lines. Or
bit less when using a compact notation (although the lines become longer).
When one event is added, we have to update at \(E\) distinct locations.
Some use a revered approach: fist switch on the event, then on the state. This helps when need to add one event;
as we only have to add \(2*S\) lines in 1 place – but fails when we need to add a state.
Some languages support a “table” approach. Mathematical, the FSM-rules can be given in a table with state and
input on the axes. The next state and the transition-action is filled-in in the cell. This results in compact (and
easy to maintain) data-structure; but needs some generic code – which is hardly ever generic, as there many variants.
Last & least, there are many “OO” templates [1]; where inheritance is used to distribute code over many subclasses and files. It
helps at bit, but only limited – as the many available alternatives already show.
Kinds of FSMs¶
The theory of FSMs is old: it predates modernd computers. With a few memory-cells and some relays (or other
combinational logic) one can build an “electronic FSM”. Even there is lot of theory available it is often assuming you
are using such electronic-one – or even only mathematical model.
This post will not repeat all that; we give a short overview, focusing on what we need for a SW-FSM and with many
(wikipedia) links for more theory.
More vs Mealy¶
Most FSM-theory is already developed in the 1950ties, by Moore and Mealy; both have a machine named to
them. Conceptually, the have equal power –meaning a Moore machine can’t do more as a Mealy machine, nor the
other-way around. But the Mealy typically has less states – which can be relevant for SW-Developers.
Hardware-developers typically prefers the Moore machine, as it is safer – for SW this advantage does not exist.
The big distinction is actions. They can depend both on the (current) state and the input – at least in a
Mealy machine. In a Moore machine the action may depend only on the state.
In the diagram (and in code) the difference is where the actions are located. When they are “on” the arrows –that
is: a combi of the current-state and the input– then it is a Mealy; when they are “in” the state (only) it’s a Moore
machine. (as the input does not directly influence the action).
For SW-FSMs we can also differentiate (Moore machines) between Entry and Leave actions; this does not apply in
electronics, nor in the old concept – they are not event-driveren (but level-active: there is an output as long as the
state is active).
And often, SW-FSMs use both Moore and Mealy kind of actions; which is fine.
FSM vs NFA¶
Most developers ony know the deterministic FSM: it has only one next state for a given current state
and input and can’t switch to another state without an input. There are also non-deterministic
FSMs (NFA), however. When a (at least one) input-sequence can lead to more-as-one states, the FSM is a NFA!
Despite that a NFA can’t be realised directly and is mathematically equivalent to a FSM, they have more
expressions-power: the table to describe them can be shorter! They are also used to implement regular-expressions
In the NFA-theory the input-sequence is ‘valid’ as there is a path (of internal states) that is valid; the others options are ignored. It kind of magic: we just assume the NFA gambles correctly which path to follow. For mathematics that will do; the practical issues, that we as engineers need to solve, is not there concern.
Transformations¶
We could be tempted to implement a NFA by using lookahead; but there easier ways as the same theory gives us. It is possible to “transform” (rebuild) a FSM into another kind. We can transform a Mealy into a Moore machine, or back. That is easy: just a bit of mathematics …
The same for a NFA. To implement a NFA, we can transform it into a deterministic FSM first. Again, this uses a
well-know (old, 1959) algorithm, that calculates super-sets
and constructs a new FSM. That, newly constructed (deterministic) FSM can have up-to \(S**2\) states and lot of
rules. It might sound complicated, But, with a lot of patience everybody can do this (manually) by following some
simple steps.
Would’t it be great when those transformations can be applied automatical? Then we can describe the FSM in the most conviant
way. And the computer will convert it into one that is deterministic and easy to execute [2] …
Epsilon transitions¶
Another interesting concept are the \(\epsilon\)-transitions –even less known by programmers. Then we allow rules
with state-transition without input. This makes the FSM always a NFA; as we can’t predict when/whether this
None input happens.
Again, it’s main use is to make the “FSM-table” shorter – albeit one has to add those \(\epsilon\)-rules into the
table!
A curious transition is the “instantly \(\epsilon\)-transition”, where no other rules are allowed (for states
that has uses it). As its needs no input, we have designed a NFA. However, as it is the only possibility and the spec
is that this \(\epsilon\)-input happens directly, it’s easy to implement in software: when state==C: {
state:=N; act_appropriate(); }.
This is often easier then removing that state and combining the actions (one step back in all paths). And quite popular
by SW-developers – one of the few places where the practise is smoother then the formal theory.
More energetic FSMs¶
As described above a non-deterministic NFA has more expression-power then a deterministic FSM and can be converted into a deterministic FSM automatically. This makes designing a FSM more easy. Likewise, there are more relative new know-how to make the job of the (SW) developers easy. We mention a few and link to more theory.
Statecharts¶
Classically, a FSM has atomic states only. In 198X a OO-variant of was invented called the “statechart diagram”, by David Harel. This is also know as UML-FSM, or
“UML statechart”. Aside of being “OO” it has a few smart concepts, that makes defining a FSM easier. We give you the
most relevants two.
Hierarchically superstates¶
When we study (or define) a system we typically start with a few “main statuses”: the system can be off,
working halted or in-error, by example. And we change mode with a few event as TurnOn
TurnOff, and InteralError. The ‘off’-state is quite clear, but how about ‘on’? And perhaps the are a few steps
between off and on.
We can solve this by adding more states In almost all of those of those states, an event as TurnOff can be
expected, and in those cases it should result in off –as before.
This make the FSM bigger and so less pleasant to design and maintain. Wouldn’t it be great to a kind generic “on-state” with one
generic TurnOff event? And have kind of sub-state of “on-state” that can implement the details?
With hierarchically superstates this is possible. One groups a set of states together and call that group a
superstate. One even repeat that process, and add higher-level group – or most developers prefer: zoom in and create
“sub” states within a state.
So the on state is kind of split into booting, warming-up and operational. And
operational contains do-prog_1, do-prog_2, do-prog_3, ect. And in all cases the
event TurnOff will turn-off the system – but you only need to add one rule!
Concurrent states (Orthogonal regions)¶
Concurrent states are more complex as super/subs-states. It are kind of local states are active
simultaneously. Wikipedia has a nice example
with the num-lock and caps-lock key: both change state – one to select capital on/of, and one to prefer arrow over
number – but those states are independent and concurrent.
Again, the advantage is it makes the “FSM table” shorter and better to maintain.
All kind of actions¶
For a SW-designer the main difference between a Moore and a Mealy is where to put actions, as described above. But why choose? In software it possible to use both Mealy actions (‘on’ the transition) as well as Moore actions (‘in’ a state). And we can even use ‘Entry’ and ‘Leave’ (or exit – but that has the same 1-character abbreviation).
When using nested-stated we can define all of those kind-of actions on all levels. David Harel was so kind to define
the sematics. Such that we now agree on the order in which the rules and actions should be executed, when many
are valid. The result is quite simple: see UML-FSM for the “transition execution sequence”.
Castle: Build-in FSM syntax¶
After all this theory and seeing all options, we call conclude “the best programming-language (for system engineers),
ever” needs to have build-in suport for all those options.
We want do program Finit State Machines directly. Not implement the details, but just describe how the FSM (or NFA)
should behave; the computer can fill in the details – all theory does exit (for years)!
In Castle one can defines FSM directly in code. As argued above FSMs and the state (design) pattern are wildly used and there a no excuses to not support that in a modern programming-language. Castle will have syntax this For the same reason, there is no need to restrict the syntax to one kind of FSM (including the NFA), or prefer one kind of actions above others. Castle will have syntax support for “all” options (unless this conflicts with other language-rules). Tip non deterministic rules are not excluded Having syntax support for non-deterministic NFA rules does not imply the “compiler” will resolves all conflicts (see e.g. [#converted_actions]). But those potential conflicts will not restrict the Castle syntax. Compare this by “devision by zero”. Everybody know that isn’t possible, but no language (syntax) will disallow
it. But a compiler may warn for it.
|
To clarify Castle has generic FSM synt... (U_FSM_Syntax) even more. Castle will support:
This list is not restrictive, and may be extended |
Tip
Once …
Having syntax-support is meaningless without the proper compile/run-time support. That however is not demand is
thise needs. One may expect that early implementations of the Castle-compiler can “parse” all syntax, but ony really
compiler (and/or optimise) the easier parts of NFA.
Once, all will be fully supported!
Footnotes