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ΠΡΠΎΡΡΠΎΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ ΠΏΠΎΠΊΡΡΡΠΈΡ Π΄Π»Ρ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΡΡ ΡΡΠ΅ΡΡΠΈΠΊΠΎΠ²ΡΡ ΡΠΈΡΡΠ΅ΠΌ
An algorithm for solving the coverability problem for monotonic counter systems is presented. The solvability of this problem is well-known, but the algorithm is interesting due to its simplicity. The algorithm has emerged as a simplification of a certain procedure of a supercompiler application (a program specializer based on V.F. Turchin's supercompilation) to a program encoding a monotonic counter system along with initial and target sets of states and from the proof that under some conditions the procedure terminates and solves the coverability problem.ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ ΠΏΠΎΠΊΡΡΡΠΈΡ Π΄Π»Ρ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΡΡ
ΡΡΠ΅ΡΡΠΈΠΊΠΎΠ²ΡΡ
ΡΠΈΡΡΠ΅ΠΌ. Π Π°Π·ΡΠ΅ΡΠΈΠΌΠΎΡΡΡ ΡΡΠΎΠΉ Π·Π°Π΄Π°ΡΠΈ Ρ
ΠΎΡΠΎΡΠΎ ΠΈΠ·Π²Π΅ΡΡΠ½Π°, Π½ΠΎ Π΄Π°Π½Π½ΡΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΠΈΠ½ΡΠ΅ΡΠ΅ΡΠ΅Π½ ΡΠ²ΠΎΠ΅ΠΉ ΠΏΡΠΎΡΡΠΎΡΠΎΠΉ. ΠΠ½ Π²ΠΎΠ·Π½ΠΈΠΊ ΠΈΠ· ΡΠΏΡΠΎΡΠ΅Π½ΠΈΡ Π½Π΅ΠΊΠΎΡΠΎΡΠΎΠΉ ΠΈΡΠ΅ΡΠ°ΡΠΈΠ²Π½ΠΎΠΉ ΠΏΡΠΎΡΠ΅Π΄ΡΡΡ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ ΡΡΠΏΠ΅ΡΠΊΠΎΠΌΠΏΠΈΠ»ΡΡΠΎΡΠ° (ΡΠΏΠ΅ΡΠΈΠ°Π»ΠΈΠ·Π°ΡΠΎΡΠ° ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌ, ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΠΎΠ³ΠΎ Π½Π° ΠΌΠ΅ΡΠΎΠ΄Π΅ ΡΡΠΏΠ΅ΡΠΊΠΎΠΌΠΏΠΈΠ»ΡΡΠΈΠΈ Π.Π€. Π’ΡΡΡΠΈΠ½Π°) ΠΊ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ΅, ΠΊΠΎΠ΄ΠΈΡΡΡΡΠ΅ΠΉ ΡΡΠ΅ΡΡΠΈΠΊΠΎΠ²ΡΡ ΡΠΈΡΡΠ΅ΠΌΡ ΠΈ Π½Π°ΡΠ°Π»ΡΠ½ΠΎΠ΅ ΠΈ ΡΠ΅Π»Π΅Π²ΠΎΠ΅ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²Π° ΡΠΎΡΡΠΎΡΠ½ΠΈΠΉ, ΠΈ ΠΈΠ· Π΄ΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΡΡΡΠ²Π°, ΡΡΠΎ ΠΏΡΠΈ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΡ
ΡΡΠ»ΠΎΠ²ΠΈΡΡ
ΡΡΠ° ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ° Π·Π°Π²Π΅ΡΡΠ°Π΅ΡΡΡ ΠΈ ΡΠ΅ΡΠ°Π΅Ρ Π·Π°Π΄Π°ΡΡ ΠΏΠΎΠΊΡΡΡΠΈΡ