LMU ☀️ CMSI 3801
THEORIES OF COMPUTER AND HUMAN LANGUAGES
Quiz 2
  1. For each of the four main theories of computation, state their primary concern in five words or less each. 
    Language Theory ________________________________________
Automata Theory ________________________________________
Computability Theory ________________________________________
Complexity Theory ________________________________________
  2. Write a Lambda Calculus expression for the function that raises its argument to itself.
  3. Evaluate $|\varepsilon|$.
  4. The concatenation of two languages $L_1$ and $L_2$ is $L_1L_2 = \{xy \;|\; x \in L_1 \wedge y \in L_2\}$. Repeated concatenation uses superscripts: $L^0 = \{\varepsilon\}$, $L^1 = L$, $L^2 = LL$, $...$, $L^{k+1} = LL^k$. Let $L = \{ w \in \{0,1\}^* \mid w = w^R \}$. Check all that are true:
    • $\varepsilon \in L$
    • $101 \in L$
    • $101 \in L^2$
    • $1010 \in L^2$
    • $01101101110 \in L^*$
  5. Given the grammar with one rule $s \longrightarrow (\texttt{"("}\;s\;\texttt{")"})^*$, give a derivation for the string ()().
  6. Given the grammar with one rule $s \longrightarrow (\texttt{"("}\;s\;\texttt{")"})^*$, give a derivation tree for the string ()().
  7. What does it mean for a grammar to be ambiguous? Choose the only correct answer.
    • A language that is Type-2 or Type-3
    • A string in the language accepted by the grammar can be derived multiple ways
    • A string in the language accepted by the grammar has multiple parse trees
    • The grammar has nested * operations.
  8. Draw a “nested circles” diagram (showing set containment) for the following language families: REG, RE, FD, CF, CS. These stand for regular, recursively enumerable, finitely describable, context-free, and context-sensitive languages, respectively.