Eckhard Bick - VISL

Though Finite State Machines (FSM) are fast, finite and efficient, they have a number
of serious shortcomings, due to the low power of the grammar types they represent:
* An FSM’s memory is very short - once a transition is made, the network only
looks at paths departing from that node, and its choice will not be conditioned by how
the algorithm got there. The NP-section of the FSM in the above example can thus not
be used for an NP-subject (by adding a direct path from S to NP, and a ‘v’-path from NP
to VP), because the FSM would confuse subject-NP and object-NP, trying, for example,
a verb-path also after having used the NP-section for object. Therefore two separate NPsections
have to be incorporated into the FSM, for subject and object, linked to S and
VP, respectively. For a similar reason, the co-ordinating conjunction path in the
example is problematic, since it doesn’t distinguish between adding am NP as coordinated
object or as subject for a co-ordinated sentence. To make the distinction,
different “conjunct networks” would have to be inserted into the network right after S
and, and before the NP node, containing conjuncted copies of the relevant network
sections. Thus, an FSM’s complexity can grow enormously for long sentences with
heavy subordination and co-ordination.
* Regular grammars cannot express inflexional agreement as such, - they’d have to
run the whole network or large sections in many parallel versions, one for every
instantiation of every category. This is why unification grammars have to be level 2
grammars (context free grammars), where no restrictions apply to the right side of a
production. Number- and gender-arguments, for example, can be thought of as
“affixes” 95 , attached as additional affix-symbols to the “normal” symbols, both allowing
for either terminal or non-terminal symbols. Number-agreement can then be added to an
ordinary PSG rule by inserting an affix-variable for number in the rewriting chain of
symbols:
regular grammar: S -> pron VP
context free grammar: S -> pron number VP number
Since the ‘number’-variable has to be instantiated with the same value in both places,
the production cannot be produced by simply working step-by-step from left to right.
By comparison, the difference between context free and context sensitive grammars is
more subtle - at least when applied to natural languages. Context sensitive rules can
usually be rewritten as one or more context free rules. A routinely quoted counter
95 For Portuguese, I have worked with the AGFL formalism (Affix Grammars over a Finite Lattice), as described in (Koster,
1991).
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