Why a Digital Clock is Decidable
Finite State System: A digital clock has a finite, albeit large, number of possible states . A typical clock tracks seconds (0-59), minutes (0-59), hours (0-23 or 1-12 with AM/PM), and potentially date information. The total number of unique configurations (states) is finite. Systems with a finite number of states are generally decidable [3].
Deterministic Behavior: The clock's transitions between states are predictable and governed by fixed rules (e.g., after 59 seconds, the seconds reset to 0, and the minutes increment by 1) . This determinism allows for predictable analysis of its behavior.
Programmatic verification of a digital clock typically involves treating it as a finite state machine (FSM) or using formal verification techniques Modeling as a Finite State Machine /Model Checking
Theorem Proving: Use interactive theorem provers (e.g.,
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