{
  "translations": {
    "en": {
      "ex1": {
        "type": "multiple",
        "description": "Example: $\\Sigma=\\{a, b, c\\}$, $\\Gamma = \\{0,1\\}$.<br/>The homomorphism function is: $h(a) = 11$, $h(b) = 00$, and $h(c) = 0$.",
        "question": "What is the value of $h(bc)$?",
        "answer": "$000$",
        "choices": ["$11$", "$00$", "$0$", "$000$", "$1100$", "$1100^*$"]
      },
      "ex2": {
        "type": "multiple",
        "description": "Example: $\\Sigma=\\{a, b, c\\}$, $\\Gamma = \\{0,1\\}$.<br/>The homomorphism function is defined as: $h(a) = 11$, $h(b) = 00$, and $h(c) = 0.$",
        "question": "What is the value of $h(ab^*)$?",
        "answer": "$11(00)^*$",
        "choices": ["$11$", "$00$", "$0$", "$000$", "$1100$", "$1100^*$", "$11(00)^*$"]
      },
      "ex3": {
        "type": "multiple",
        "description": "Example: $\\Sigma=\\{a, b\\}$, $\\Gamma = \\{a,b,c\\}$.<br/>The homomorphism function is defined as: $h(a) = ab$, $h(b) = bbc$.",
        "question": "What is the value of $h(aa)$?",
        "answer": "$abab$",
        "choices": ["$ab$", "$bbc$", "$abbbcab$", "$bbcad$", "$abbbc$", "$abab$"]
      },
      "ex4": {
        "type": "multiple",
        "description": "Example: $\\Sigma=\\{a, b\\}$, $\\Gamma = \\{a,b,c\\}$.<br/>The homomorphism function is defined as: $h(a) = ab$, $h(b) = bbc$.",
        "question": "What is the value of $h(aba)$?",
        "answer": "$abbbcab$",
        "choices": ["$ab$", "$bbc$", "$abbbcab$", "$bbcad$", "$abbbc$", "$abab$"]
      },
      "ex5": {
        "type": "multiple",
        "description": "Example: $\\Sigma=\\{0, 1\\}$, $\\Gamma = \\{a, b\\}$.<br/>The homomorphism function is defined as: $h(0) = ab$, $h(1) = \\lambda$.",
        "question": "What is the value of $h(01010)$?",
        "answer": "$ababab$",
        "choices": ["$ab$", "$bb$", "$ababab$", "$bbad$", "$abbb$", "$abab$"]
      },
      "regex1": {
        "type": "multiple",
        "description": "Example: $\\Sigma=\\{a, b\\}$, $\\Gamma = \\{b, c, d\\}$.<br/>The homomorphism function is defined as: $h(a) = db$, $h(b) = cc$.",
        "question": "What is the value of $h((a + b^*)^*)$?",
        "answer": "$(db + (cc)^*)^*$",
        "choices": ["$(a + b^*)^*$", "$(db + b^*)^*$", "$(db + c^*)^*$", "$(db + (cc)^*)^*$"]
      },
      "regex1b": {
        "type": "multiple",
        "description": "Example, $\\Sigma=\\{a, b\\}$, $\\Gamma = \\{b, c, d\\}$.<br/>The homomorphism function is defined as: $h(a) = db$, $h(b) = cc$.",
        "question": "The result for $h((a + b^*)^*)$ is $(db + (cc)^*)^*$. Is $(db + (cc)^*)^*$ a regular expression?",
        "answer": "Yes",
        "choices": ["Yes", "No"]
      },
      "regex1c": {
        "type": "multiple",
        "description": "Example, $\\Sigma=\\{a, b\\}$, $\\Gamma = \\{b, c, d\\}$.<br/>The homomorphism function is defined as: $h(a) = db$, $h(b) = cc$.",
        "question": "[T|F] The resulting language is regular.",
        "answer": "True",
        "choices": ["True", "False"]
      }
    }
  }
}