In exams: Automatic Generation of Exams in R

# use the same graphics type (pdf, svg, png) as the current xweave() call
typ <- match_exams_device()

## tikz automaton code with two placeholders
automaton <- '
\\begin{tikzpicture}[shorten >=1pt,node distance=2cm]
\\node[state, initial%s] (A)              {A};
\\node[state%s]          (B) [below=of A] {B};
\\node[state%s]          (C) [right=of A] {C};
\\node[state%s]          (D) [below=of C] {D};
\\path[->] (A) edge [bend left=20] node [right] {1} (B)
           (A) edge [bend left=20] node [above] {0} (C)
           (B) edge [bend left=20] node [left]  {1} (A)
           (B) edge [bend left=20] node [above] {0} (D)
           (C) edge [bend left=20] node [right] {1} (D)
           (C) edge [bend left=20] node [below] {0} (A)
           (D) edge [bend left=20] node [left]  {1} (C)
           (D) edge [bend left=20] node [below] {0} (B);
\\end{tikzpicture}
'

## sample acceptance state and insertions
accept <- sample(c("A", "B", "C", "D"), 1)
automaton <- sprintf(automaton,
  if(accept == "A") ", accepting" else "",
  if(accept == "B") ", accepting" else "",
  if(accept == "C") ", accepting" else "",
  if(accept == "D") ", accepting" else "")

## assure unique sequences
ok <- FALSE
while(!ok) {

## five random sequences
sequences <- replicate(5,
  sample(0:1, sample(4:7, 1), replace = TRUE),
  simplify = FALSE
)

## check whether even or odd sequences lead to accepting state
even0 <- accept %in% c("A", "B")
even1 <- accept %in% c("A", "C")
n1 <- sapply(sequences, sum)
n0 <- sapply(sequences, length) - n1
sol <- (even0 == (n0 %% 2L < 1L)) & (even1 == (n1 %% 2L < 1L))
sequences <- sapply(sequences, paste, collapse = "")

ok <- all(!duplicated(sequences)) && any(sol) && any(!sol)
}

Question

Consider the following automaton with initial state A and accepting state r accept: \

include_tikz(automaton, name = "automaton", format = typ, markup = "markdown",
  library = c("automata", "positioning"),
  width = "5cm")

Which of the following sequences are accepted?

answerlist(sequences, markup = "markdown")

Solution

The given automaton accepts input strings which consist of an r if(even1) "even" else "odd" number of ones and r if(even0) "even" else "odd" number of zeros.

answerlist(ifelse(sol, "Accepted", "Not accepted"), markup = "markdown")

Meta-information

exname: Automaton extype: mchoice exsolution: r mchoice2string(sol)

exams documentation built on Nov. 14, 2022, 3:02 p.m.