## EX and NEX Searches

Results from an EXACT (EX) search are a subset of AND, NR, XNR, and AD results.

{AND} ⊇ {NR} ⊇ {XNR} ⊇ {AD} ⊇ {EX} (1)

A subtractive complement, relative to AND, is also defined.

{NEX} = {AND} - {EX} (2)

This is depicted in the next figure.

Figure 1. EXACT results as a subset of AND results.

The blue region represents the number of EX matches and the pink one the number of EX nonmatches or NEX. The sum of both regions represents the total number of AND results. So NEX is the subtractive complement of EX, relative to the AND set.

In other words, the blue region corresponds to the number of AND results that match an EXACT search whereas the pink region corresponds to the number of AND results that do not match said search. We could have computed this complement relative to AD, but we elected not to do that.

### Applications to IR

In our implementation, an EXACT search matches all query terms in a strict order and as submitted.

When declared in a query, the 'EX' abbreviation interpret the query as a strict sequence. One can also double quote all search terms to invoke this type of search, vary much the way you run exact searches in other search engines (1). Thus, the queries

EX:w1 w2...(3)

or

"w1 w2..."(4)

instruct the platform to find documents matching the w1 w2... term sequence.

As a result, an EX search can find documents matching a sequence of terms, phrases, or clauses. It is the preferred mode for searching for titles, names, and short passages.

This is illustrated in Figure 2 for a two-term query.

Figure 2. Representation matching an exact sequence of terms.

Notice that from Eq (1) the fraction of AND results that match a term sequence is

{EX}/{AND}(5)

This is a search signal in the sense that it estimates how popular is a term sequence over a set of document matching said terms in any order.

### Final Remarks

Minerazzi supports the EX search mode and its subtractive complement, relative to the AND mode. This mode helps users discriminate between AND results based on a word order criterion that is defined at query time.

### References

- Google. (Accessed on 1-16-2014).Advanced Search.
- Online Library Learning. (Accessed on 1-16-2014). Exact Search.