Anytime Algorithms for Non-Ending Computations

Anytime algorithms exchange execution time for quality of results [8]. Anytime algorithms can be executed in two modes: either by being given a contract time (a set amount of time to execute), or an interruptible method. To improve the solution, anytime algorithms can be continued after they have halted. Instead of correctness, an anytime algorithm returns a result with a “quality measure” which evaluates how close the obtained result is to the result that would be returned if the algorithm ran until completion. Standard anytime algorithms eventually stop, albeit in a prohibitively long time. Following Manin [11] we use a more general form of anytime algorithm as an approximation for a computation which may not end. The proposed anytime algorithm for the halting problem works in the following way: to test whether a program eventually stops we first compute a temporal bound — the interruptible (stopping) condition — and execute the program for that specific time. If the computation stops then the program was proved to halt; if the computation does not stop, then we declare that the program never stops and evaluate the error probability. By