0

I am going through the paper 'SPEECH RECOGNITION WITH WEIGHTED FINITE-STATE TRANSDUCERS' (hbka.pdf - https://cs.nyu.edu/~mohri/pub/hbka.pdf)

At page 9, and figure 6

I do not understand how 6 a) figure be considered for 'non-determinism'.

[Here ae/k t represents the triphonic model for ae with left context k and right context t. This transition is considered as non-deterministic. Why?]

The differences between transitions that are termed 'non-deterministic' and 'deterministic' are

  1. Nondeterministic transitions allow (epsilon transitions) a transition to happen between states without any input symbol consumption and/or any output symbol generation.

This is especially useful where the transducer is supposed to output English word morphological description from the input English word, like in cities -> city -PL. Here there are transitions between states where you input and output the same alphabet. But when you input i or e you need not output anything and in the final transition for input s you would output y -PL

So, I understand the need for epsilon transitions. I also understand that non-deterministic transitions are when multiple transitions for same input label can exist. This could lead to ambiguity and hence supports the name 'non-deterministic'.

  1. Deterministic transitions are the very opposite of the above. No multiple transitions for same input label; hence every transition is unique. No epsilon transitions.

With this limited knowing, I could not decipher why a transition could ever be called 'non-deterministic' when you have provided the context. Here ae/k t represents the triphonic model for ae with left context k and right context t. This transition is considered as non-deterministic. Why?

The main idea of providing context is to remove the ambiguity.

Anantha Krishnan
  • 13
  • 3

1 Answers1

0

The text to the right of the colon : is the output of the transition, not its input; so it doesn't help determine which transition to take, but rather, you need to take the right transition in order to get the right output.

ruakh
  • 175,680
  • 26
  • 273
  • 307
  • I know that the transition is in this form input label: output label /it's context. However, I do not see why such a transition be called as 'non-deterministic'. – Anantha Krishnan Jul 07 '23 at 04:37
  • @AnanthaKrishnan: Re: "I know that the transition is in this form input label: output label /it's context": That's not correct. There aren't three fields (input label, output label, context), but rather, only two fields (input label, output label). The context is part of the output label. Re: "I do not see why such a transition be called as 'non-deterministic'": It's "non-deterministic" in that it belongs to a non-deterministic transducer. The transducer is non-deterministic because every transition out of state *k,ae* has the same input label *ae*. – ruakh Jul 07 '23 at 06:16
  • Thanks! So, you mean that in the given diagram, only the transition diagram is given but not the entire tree (Transducer). It was my mistake to refer to path/transition as 'non-deterministic' as only the transducer as a whole can be called as 'deterministic' or 'non-deterministic'. – Anantha Krishnan Jul 07 '23 at 07:47