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Formal equivalence is often more goal than reality, if only because one language may contain a word for a concept which has no direct equivalent in another language. In such cases, a more dynamic translation may be used or a neologism may be created in the target language to represent the concept (sometimes by borrowing a word from the source ...
In formal language theory, weak equivalence of two grammars means they generate the same set of strings, i.e. that the formal language they generate is the same. In compiler theory the notion is distinguished from strong (or structural) equivalence, which additionally means that the two parse trees [clarification needed] are reasonably similar in that the same semantic interpretation can be ...
In 1964, [citation needed] Eugene Nida described translation as having two different types of equivalence: formal and dynamic equivalence. [14] Formal equivalence is when there is focus on the message itself (in both form and content); [15] the message in the target language should match the message in the source language as closely as possible ...
For more information, see "Dynamic and formal equivalence." Nida also developed the componential analysis technique, which split words into their components to help determine equivalence in translation (e.g. "bachelor" = male + unmarried). This is, perhaps, not the best example of the technique, though it is the most well-known.
A formal equivalence check can be performed between any two representations of a design: RTL <> netlist, netlist <> netlist or RTL <> RTL, though the latter is rare compared to the first two. Typically, a formal equivalence checking tool will also indicate with great precision at which point there exists a difference between two representations.
Equivalence relations are a ready source of examples or counterexamples. For example, an equivalence relation with exactly two infinite equivalence classes is an easy example of a theory which is ω-categorical, but not categorical for any larger cardinal number.
The minimal automaton accepting our language would have three states corresponding to these three equivalence classes. Another immediate corollary of the theorem is that if for a language the relation has infinitely many equivalence classes, it is not regular. It is this corollary that is frequently used to prove that a language is not regular.
For example, Robert Pinsky is reported to have used a literal translation in preparing his translation of Dante's Inferno (1994), as he does not know Italian. Similarly, Richard Pevear worked from literal translations provided by his wife, Larissa Volokhonsky, in their translations of several Russian novels.