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Some loops can be shown to always terminate or never terminate through human inspection. For example, the following loop will, in theory, never stop. However, it may halt when executed on a physical machine due to arithmetic overflow : either leading to an exception or causing the counter to wrap to a negative value and enabling the loop ...
The variant's value must decrease during each loop iteration but must never become negative during the correct execution of the loop. Loop variants are used to guarantee that loops will terminate. A loop invariant is an assertion which must be true before the first loop iteration and remain true after each iteration.
The test for i < len is still present, but it has been moved outside the loop, which now contains only a single test (for the value), and is guaranteed to terminate due to the sentinel value. There is a single check on termination if the sentinel value has been hit, which replaces a test for each iteration.
Let be the state at time .For a decision that begins at time 0, we take as given the initial state .At any time, the set of possible actions depends on the current state; we express this as (), where a particular action represents particular values for one or more control variables, and () is the set of actions available to be taken at state .
The halting problem is a decision problem about properties of computer programs on a fixed Turing-complete model of computation, i.e., all programs that can be written in some given programming language that is general enough to be equivalent to a Turing machine. The problem is to determine, given a program and an input to the program, whether ...
The "Markov" in "Markov decision process" refers to the underlying structure of state transitions that still follow the Markov property. The process is called a "decision process" because it involves making decisions that influence these state transitions, extending the concept of a Markov chain into the realm of decision-making under uncertainty.
The control action is the switching on/off of the boiler, but the controlled variable should be the building temperature, but is not because this is open-loop control of the boiler, which does not give closed-loop control of the temperature. In closed loop control, the control action from the controller is dependent on the process output.
To determine if a causal loop is reinforcing or balancing, one can start with an assumption, e.g. "Variable 1 increases" and follow the loop around. The loop is: reinforcing if, after going around the loop, one ends up with the same result as the initial assumption. balancing if the result contradicts the initial assumption.