#Finite automaton series#

Note how the input to 'delay' includes 'v', a value derived from its output. T0 = UTCTime (ModifiedJulianDay 0) (secondsToDiffTime 0) Prev NominalDiffTime -> a (UTCTime, Double) (Double, Double)ĭt = fromRational $ toRational $ diffUTCTime t2 t1 (Note: again, untested code) recognise :: Auto Char Bool Automaton is an instance of all the interesting arrow classes, including Loop and Circuit, so you can get access to previous values by using delay. In terms of your original question, Q =, X = Char, delta is function application, and F is the state transition returning True (rather than having an 'accepting state' I've used an output transition with an accepting value).Īlternatively you can use Arrow notation. When the desired symbol is found, then the transition occurs. It takes the string of symbol as input and changes its state accordingly. State1 c = if c = 'a' then (False, state2) else (False, state1) Finite automata are used to recognize patterns. (Note: untested code) state1, state2 :: Auto Char Bool

#Finite automaton series#

For instance, here is a state machine to recognise the regexp 'a+b' (that is, a series of at least one 'a' followed by a 'b'). You can use this directly by writing a function for each state that takes an argument and returns the result and the next function. In other words an automaton is a function that takes an input and returns a result and a new automaton.

Substituting (->) for 'a' in the Automaton definition and using infix notation you can see this is roughly equivalent to: newtype Auto b c = Automaton (b -> (c, Auto b c)) Which uses functions as the underlying arrow. Automata editor About Automata editor is vector editor for drawing finite automata according to VauCanSon-G format (a LaTeX package). In the simplest case you can write type Auto = Automaton (->) This is a bit confusing because its an arrow transformer. Finite Automata An automaton with a finite number of states is called a Finite Automaton (FA) or Finite State Machine (FSM). The type looks like this newtype Automaton a b c = Automaton (a b (c, Automaton a b c))

On a different note, the alphabet is most definitely necessary: it is how the automaton receives input.Ĭheck out the module in the 'arrows' package. maybeToList ( join is from Data.Monad and maybeToList is from Data.Maybe). an empty list, and so there doesn't need to be any special handling of the Maybe beyond a call to join. Non-deterministic automata work well with the map option, because a failed look-up is the same as having no state to go to, i.e. there is always an entry in the map for any possible (Q,X) tuple and so the look-up never fails (never returns Nothing)). from user input), then storing delta as a map (and possibly doing the function conversion as above) and having an appropriate input validation that guarantees correctness so that fromJust is safe (i.e. If you are constructing the automata at run time (e.g. If you are constructing the automata at compile time (and so know the possible states and can have them encoded as a data type), then using the function version gives you better type safety, as the compiler can verify that you have covered all cases. Definition 3.1 (Finite Automaton): A finite automaton (FA in short) is a five-tuple (Q,, , q0, qf) where (i) Q is a finite nonempty set of states. (Or the appropriately curried version of the look-up function for whatever mapping type you are using.) Note that these two approaches are essentially equivalent, one can convert from the map version to a function version (this is slightly different due to an extra Maybe from the lookup call) relatively easily delta_func q x = (q,x) delta_map In a formal way it is also known as Finite State Machine (FSM) or Transducer. A finite automata with output is similar to finite automata (FA) except that the additional capability of producing output. using Data.Map, or if your states/alphabet can be indexed by ascending numbers Data.Array or Data.Vector. Finite automata can also be used as an output device. An explicit function delta :: Q -> X -> Q (or as appropriate) as Sven Hager suggests.Implementing a finite state machine is quite straightforward.