Finite State Machines (FSM) Quiz Quiz

Challenge your grasp of Finite State Machines (FSMs) with questions about definitions, core concepts, practical examples, and differentiating FSM types. Assess your knowledge on how FSMs are used in computing, automata theory, and system design.

1. Basics of Finite State Machines

   Which of the following best describes a Finite State Machine (FSM) in the context of computational models?

   1. A process that only uses random transitions between outputs
   2. A model that operates without defined states or rules
   3. A mathematical model with a finite number of states, transitions, and inputs
   4. A device with an infinite set of possible configurations

   Explanation: A Finite State Machine (FSM) is defined as a mathematical model consisting of a finite number of states, transitions between those states, and a set of possible inputs. The distractor suggesting 'an infinite set of possible configurations' is incorrect, as FSMs are finite by definition. The option claiming there are no defined states or rules is incorrect since states and transitions are essential components. Random transitions would not create a well-defined machine, making the last distractor inappropriate.

2. FSM Application Example

   Consider a vending machine that dispenses a product only after receiving exactly two coins. Which type of finite state machine could most simply represent this scenario?

   1. A Mealy machine
   2. A Pushdown automaton
   3. A Moore machine
   4. A Turing machine

   Explanation: A Moore machine outputs solely depend on its state, making it suitable for a vending machine where output (dispensing) occurs in a specific state after two coins are received. A Mealy machine’s output depends on both states and inputs, which could complicate the design for this simple scenario. Turing machines and pushdown automata are more powerful computational models and not required for this basic application, making those distractors less suitable.

3. Recognizing FSM Types

   What distinguishes a Mealy machine from a Moore machine in finite state machine theory?

   1. Output of a Mealy machine depends on both current state and input, while a Moore machine’s output depends only on the state
   2. A Moore machine can use memory tape, but a Mealy machine cannot
   3. Mealy machines always have more states than Moore machines for any given problem
   4. Mealy machines have transitions with no outputs

   Explanation: The primary difference is that a Mealy machine’s output is a function of both its state and its inputs, while a Moore machine’s output depends solely on the current state. The claim that Mealy machines always have more states isn’t generally true. Memory tape usage applies to Turing machines, not Moore machines. All FSM transitions can generate outputs, so the last distractor is incorrect.

4. FSM Accepting Strings

   If a finite state machine accepts the string 'ab' but not 'aab' or 'bba', what can you infer about its language?

   1. The FSM accepts all strings of length exactly two where the first character is 'a' and the second is 'b'
   2. The FSM accepts all strings ending with 'b'
   3. The FSM accepts any string containing at least one 'a'
   4. The FSM accepts only empty strings

   Explanation: Since the FSM accepts 'ab' but not 'aab' or 'bba', this suggests it is designed to accept only strings of exact length two starting with 'a' and ending with 'b'. Accepting any string containing at least one 'a' is incorrect since 'aab' is not accepted. Accepting only empty strings is not possible since 'ab' is accepted. Acceptance of all strings ending with 'b' is also ruled out by 'bba' not being accepted.

5. FSM Transition Table Interpretation

   Given a transition table with states S0 and S1, where S0 transitions to S1 on input '1' and stays on S0 on '0', which pattern does this FSM accept?

   1. Binary strings ending with '1'
   2. Binary strings with even number of ones
   3. Binary strings that never have consecutive ones
   4. Binary strings that contain at least one '1'

   Explanation: The FSM transitions to S1 upon reading input '1', while input '0' keeps it at S0, so the machine likely accepts strings ending in '1'. The other options do not match this behavior: strings with at least one '1' would accept strings where '1' may appear anywhere, which is not implied here. An even number of ones or non-consecutive ones do not directly relate to the described transitions. The accepting criterion here is based on the last symbol.