Final answer:
An informal description and state diagrams of pushdown automata (PDA) should include input and stack alphabets, states, initial and accepting states, and transition rules with conditions and stack operations. A state diagram consists of circles for states and arrows for transitions. An example could be designing a PDA that accepts strings with an equal number of 'a's and 'b's by manipulating the stack accordingly.
Step-by-step explanation:
To provide an informal description and state diagrams for pushdown automata (PDA) for the languages in exercise 2.4, we must assume that exercise 2.4 describes specific languages. Since the precise languages are not provided, we will discuss a general approach to creating PDAs instead.
A pushdown automaton is like a finite automaton but with an added stack. This stack gives the automaton memory, allowing it to recognize some types of context-free languages, which finite automata cannot do. To describe a PDA informally, you would specify the input alphabets, the stack alphabets, the states, the initial state, the accepting state(s), and the transitions with conditions and stack operations (push and pop).
Creating a state diagram for a PDA involves drawing circles for the states, arrows for the transitions, and labels on the arrows to indicate the input being read and the stack operations. An example might be an arrow going from state S1 to state S2 with the label 'a, b → c', which would mean when an 'a' is read and a 'b' is on top of the stack, pop the 'b' and push a 'c', and then transition to state S2.
When dealing with PDAs, one common task is to design a PDA for the language L that consists of strings of 'a's and 'b's such that the number of 'a's is equal to the number of 'b's. The PDA would keep track of the difference between the count of 'a's and 'b's, pushing onto the stack for every 'a' and popping from the stack for every 'b' (or vice versa), ensuring that it only accepts the input by reaching an accepting state when the stack is empty, indicating equal numbers of 'a' and 'b'.