2 research outputs found
Mixed computation: potential applications and problems for study
AbstractMixed computation is processing of an incomplete information. Its product are a partially processed information and a so-called residual program destined to complete in sequel the processing of the remaining information. Many kinds of practical work with programs are nothing more but obtaining a residual program. We demonstrate, as an example, the application of mixed computation to compilation. Under computational approach mixed computation generalizes the operational semantics of a language by inclusion of steps which generate residual program instructions. Under transformational approach the residual program is obtained as a result of a series of so-called basic transformations of the program text. We argue that the transformational approach is more fundamental, for it allows to describe mixed computation in all its variety and moreover, to relate mixed computation to other kinds of program manipulation: execution, optimization, macroprocessing, synthesis. Such an integrated approach leads us to a transformational machine concept
Π Π·Π°Π΄Π°ΡΠ΅ ΠΌΠΈΠ½ΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½ΡΡ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌ
First-order program schemata is one of the simplest models of sequential imperative programs intended for solving verification and optimization problems. We consider the decidable relation of logical-thermal equivalence of these schemata and the problem of their size minimization while preserving logical-thermal equivalence. We prove that this problem is decidable. Further we show that the first-order program schemata supplied with logical-thermal equivalence and finite state deterministic transducers operating over substitutions are mutually translated into each other. This relationship implies that the equivalence checking problem and the minimization problem for these transducers are also decidable. In addition, on the basis of the discovered relationship, we have found a subclass of firstorder program schemata such that their minimization can be performed in polynomial time by means of known techniques for minimization of finite state transducers operating over semigroups. Finally, we demonstrate that in general case the minimization problem for finite state transducers over semigroups may have several non-isomorphic solutions.Π‘ΡΠ°Π½Π΄Π°ΡΡΠ½ΡΠ΅ ΡΡ
Π΅ΠΌΡ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌ β ΡΡΠΎ ΠΎΠ΄Π½Π° ΠΈΠ· Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΠΏΡΠΎΡΡΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½ΡΡ
ΠΈΠΌΠΏΠ΅ΡΠ°ΡΠΈΠ²Π½ΡΡ
ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌ, ΠΏΡΠ΅Π΄Π½Π°Π·Π½Π°ΡΠ΅Π½Π½Π°Ρ Π΄Π»Ρ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°Ρ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΈ Π²Π΅ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌ. ΠΡ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΠΌ ΡΠ°Π·ΡΠ΅ΡΠΈΠΌΠΎΠ΅ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠ΅ Π»ΠΎΠ³ΠΈΠΊΠΎ-ΡΠ΅ΡΠΌΠ°Π»ΡΠ½ΠΎΠΉ ΡΠΊΠ²ΠΈΠ²Π°Π»Π΅Π½ΡΠ½ΠΎΡΡΠΈ ΡΡΠ°Π½Π΄Π°ΡΡΠ½ΡΡ
ΡΡ
Π΅ΠΌ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌ ΠΈ Π·Π°Π΄Π°ΡΡ ΠΌΠΈΠ½ΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΈΡ
ΡΠ°Π·ΠΌΠ΅ΡΠ° ΠΏΡΠΈ ΡΡΠ»ΠΎΠ²ΠΈΠΈ ΡΠΎΡ
ΡΠ°Π½Π΅Π½ΠΈΡ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡ Π»ΠΎΠ³ΠΈΠΊΠΎ-ΡΠ΅ΡΠΌΠ°Π»ΡΠ½ΠΎΠΉ ΡΠΊΠ²ΠΈΠ²Π°Π»Π΅Π½ΡΠ½ΠΎΡΡΠΈ. ΠΠ°ΠΌΠΈ Π΄ΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΡΡΠ° Π·Π°Π΄Π°ΡΠ° ΡΠ²Π»ΡΠ΅ΡΡΡ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΈΡΠ΅ΡΠΊΠΈ ΡΠ°Π·ΡΠ΅ΡΠΈΠΌΠΎΠΉ. ΠΠ°Π»Π΅Π΅ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΡΡΠ°Π½Π΄Π°ΡΡΠ½ΡΠ΅ ΡΡ
Π΅ΠΌΡ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌ Ρ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠ΅ΠΌ Π»ΠΎΠ³ΠΈΠΊΠΎ-ΡΠ΅ΡΠΌΠ°Π»ΡΠ½ΠΎΠΉ ΡΠΊΠ²ΠΈΠ²Π°Π»Π΅Π½ΡΠ½ΠΎΡΡΠΈ ΠΈ ΠΊΠΎΠ½Π΅ΡΠ½ΡΠ΅ Π΄Π΅ΡΠ΅ΡΠΌΠΈΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΡΠ΅ Π°Π²ΡΠΎΠΌΠ°ΡΡ-ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°ΡΠ΅Π»ΠΈ, ΡΠ°Π±ΠΎΡΠ°ΡΡΠΈΠ΅ Π½Π°Π΄ ΠΏΠΎΠ»ΡΠ³ΡΡΠΏΠΏΠ°ΠΌΠΈ ΠΏΠΎΠ΄ΡΡΠ°Π½ΠΎΠ²ΠΎΠΊ, Π²Π·Π°ΠΈΠΌΠ½ΠΎ ΡΡΠ°Π½ΡΠ»ΠΈΡΡΡΡΡΡ Π΄ΡΡΠ³ Π² Π΄ΡΡΠ³Π°. ΠΡΡΡΠ΄Π° ΡΠ»Π΅Π΄ΡΠ΅Ρ, ΡΡΠΎ ΡΠ°ΠΊΠΆΠ΅ ΡΠ°Π·ΡΠ΅ΡΠΈΠΌΡ Π·Π°Π΄Π°ΡΠΈ ΠΏΡΠΎΠ²Π΅ΡΠΊΠΈ ΡΠΊΠ²ΠΈΠ²Π°Π»Π΅Π½ΡΠ½ΠΎΡΡΠΈ ΠΈ ΠΌΠΈΠ½ΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ Π΄Π»Ρ ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°ΡΠ΅Π»Π΅ΠΉ ΡΠΊΠ°Π·Π°Π½Π½ΠΎΠ³ΠΎ Π²ΠΈΠ΄Π°. ΠΡΠΎΠΌΠ΅ ΡΠΎΠ³ΠΎ, Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½Π½ΠΎΠΉ Π²Π·Π°ΠΈΠΌΠΎΡΠ²ΡΠ·ΠΈ Π²ΡΠ΄Π΅Π»Π΅Π½ ΠΏΠΎΠ΄ΠΊΠ»Π°ΡΡ ΡΡΠ°Π½Π΄Π°ΡΡΠ½ΡΡ
ΡΡ
Π΅ΠΌ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌ, ΠΌΠΈΠ½ΠΈΠΌΠΈΠ·Π°ΡΠΈΡ ΠΊΠΎΡΠΎΡΡΡ
ΠΎΡΡΡΠ΅ΡΡΠ²ΠΈΠΌΠ° Π·Π° ΠΏΠΎΠ»ΠΈΠ½ΠΎΠΌΠΈΠ°Π»ΡΠ½ΠΎΠ΅ Π²ΡΠ΅ΠΌΡ ΠΏΡΠΈ ΠΏΠΎΠΌΠΎΡΠΈ ΡΠ°Π½Π΅Π΅ ΠΈΠ·Π²Π΅ΡΡΠ½ΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΌΠΈΠ½ΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ Π°Π²ΡΠΎΠΌΠ°ΡΠΎΠ²-ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°ΡΠ΅Π»Π΅ΠΉ, ΡΠ°Π±ΠΎΡΠ°ΡΡΠΈΡ
Π½Π°Π΄ ΠΏΠΎΠ»ΡΠ³ΡΡΠΏΠΏΠ°ΠΌΠΈ. Π Π·Π°ΠΊΠ»ΡΡΠ΅Π½ΠΈΠΈ ΠΏΡΠΈΠ²Π΅Π΄Π΅Π½ ΠΏΡΠΈΠΌΠ΅Ρ, ΡΠ²ΠΈΠ΄Π΅ΡΠ΅Π»ΡΡΡΠ²ΡΡΡΠΈΠΉ ΠΎ ΡΠΎΠΌ, ΡΡΠΎ Π² ΠΎΠ±ΡΠ΅ΠΌ ΡΠ»ΡΡΠ°Π΅ Π·Π°Π΄Π°ΡΠ° ΠΌΠΈΠ½ΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ Π°Π²ΡΠΎΠΌΠ°ΡΠΎΠ²- ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°ΡΠ΅Π»Π΅ΠΉ Π½Π°Π΄ ΠΏΠΎΠ»ΡΠ³ΡΡΠΏΠΏΠΎΠΉ ΠΏΠΎΠ΄ΡΡΠ°Π½ΠΎΠ²ΠΎΠΊ ΠΌΠΎΠΆΠ΅Ρ ΠΈΠΌΠ΅ΡΡ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΎ Π½Π΅ΠΈΠ·ΠΎΠΌΠΎΡΡΠ½ΡΡ
ΡΠ΅ΡΠ΅Π½ΠΈΠΉ.