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Home » Computer Dictionary » Letter N » Nerode Equivalence Definition/Meaning

# Nerode Equivalence Definition/Meaning:

An equivalence relation, = N, arising in formal language theory. It is defined analogously to the Myhill equivalence by the weaker properties:

for a language L over ∑,

u = N u'

if, for all w in ∑*,

uw € L iff u'w  €  L

for a function ƒ

u = N u'

if, for all w in ∑*,

ƒ(uw) = ƒ(u'w)

Although coarser than the Myhill equivalence, it is finite only if the latter is. Unlike the latter, it gives only a right congruence:

u = N u' implies uv = N u' v

and thus does not give rise to a semigroup. The number of equivalence classes is the number of states in the minimal machine for L.

## Near by Terms:

 Network Control Protocol Negation Negative Acknowledgment (NAK) Negative Logic Nerode Equivalence Nesting Nesting Store Network Network Architecture Network Database System Network Delay Network Front End Network Virtual Terminal (NVT) Network Independent File Transfer Protocol (NIFTP)

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