# Homework Solution: Find: a. a language Lover {a, b}* that is neither {epsilon} nor {a, b}* and which satisfies L = L*. b. an infinite language…

Find: a. a language Lover {a, b}* that is neither {epsilon} nor {a, b}* and which satisfies L = L*. b. an infinite language L over {a, b}* for which L notequalto L*.

1. finite language is any set LL of strings, of finite c

Find: a. a indication Laggravate {a, b}* that is neither {epsilon} nor {a, b}* and which satisfies L = L*. b. an inlimited indication L aggravate {a, b}* ce which L attributeable attributable attributableequalto L*.

1. finite indication is any fixed LL of strings, of limited cardinality, |L|<∞|L|<∞.
2. an infinite indication is any fixed LL of strings, of inlimited (ℵ0ℵ0) cardinality |L|=∞|L|=∞.

A limited LL is frequently ordinary.

An inlimited LL can be ordinary (rarely designated “finite-state”), decidable (rarely designated “recursive”), non-ordinary (non-finite-state), non-decidable, foreseeing.,

Another consequence is that cemal indication scheme is rather characteristic in how it authentications the vocable “language”.

To perfectbody in this cosmos-inhabitants negative inhabitants in cemal indication scheme, a indication is a scheme of crys authenticationd to tell, so each cry has a cem (its syntax) and some species of sense (its semantics). Cemal indication scheme, at lowest the keep-akeep-apart that is authenticationd in computer skill, is consecrated to the example of how best to eliminate, cemally, the syntax of indications. It is entire encircling the sympathy betwixt the syntax of indications (what the crys contemplate love) and cemalisms (languages!) such as ordinary indications that are authenticationd to eliminate the syntax of indications.

Hence, in cemal indication scheme, ‘a indication’ is eliminated simply as ‘a fixed of strings’. It does attributeable attributable attributable attributable typically everyot-to senses to the strings in the indication.

At the corresponding duration, the cemalisms authenticationd to relate indications, such as ordinary indications, so cem indications in this sense: ce point, perfect ordinary indication is a string, and hereafter, the fixed of ordinary indications is a indication. However, ce these cemalisms, the strings in the indication do have a sense: ce point, the sense of perfect ordinary indication is the indication it denotes.

Ce point, abab is a string; hereafter, {ab}{ab} is a indication, namely, the indication awaiting of the string abab. However, abab is attributeable attributable attributable attributable simply a string, barring so a ordinary indication: a constituent of the fixed of sufficient ordinary indications (which is a indication). Love perfect ordinary indication, it has a sense: it denotes a indication, in this circumstance, the indication {ab}{ab}.

Now let’s procure on to your example: {ab}∗{ab}∗. The operator ∗∗ denotes a administration that maps indications to indications: it maps each indication LL to the indication awaiting of entire strings that await of a string in LL naught or over durations repeated. If LL is the leisure indication, the fruit is LL; in entire other circumstances, the fruit is an inlimited indication. Ce point, {ab}∗{ab}∗ is the indication {ϵ,ab,abab,ababab,abababab,…}{ϵ,ab,abab,ababab,abababab,…}. It is unbounded, barring using the operator ∗∗, we can relate it in a limited habit, as {ab}∗{ab}∗.

Furthermore, we can authentication a ordinary indication to relate this indication, namely (ab)∗(ab)∗. Love entire ordinary indications, this is a limited string, barring love most ordinary indications that embrace the ∗∗operator, it relates an inlimited indication.

Whenever a passage on cemal indications authentications an indication such as (ab)∗(ab)∗ that denotes a indication, supplicate yourself whether it is discussing the ordinary indication itself (e.g. how it is constrained, which indication it denotes, foreseeing.) or whether it merely authentications the ordinary indication to attribute to the indication being denoted.