Geodesic
On the expressiveness of the approach to constructing PLC-programs by LTL-specification
Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 4, pp. 507-520

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The article is devoted to the approach to constructing and verification of discrete PLC-programs by LTL-specification. This approach provides an ability of correctness analysis of PLC-programs by the model checking method. The linear temporal logic LTL is used as a language of specification of the program behavior. The correctness analysis of LTL-specification is automatically performed by the symbolic model checking tool Cadence SMV. The article demonstrates the consistency of the approach to constructing and verification of PLC programs by LTL-specification from the point of view of Turing power. It is proved, that in accordance with this approach for any Minsky counter machine can be built an LTL-specification, which is used for machine implementation in any PLC programming language of standard IEC 61131-3. Minsky machines equipollent Turing machines, and the considered approach also has Turing power. The proof focuses on representation of a counter machine behavior in the form of a set of LTL-formulas and matching these formulas to constructions of ST and SFC languages. SFC is interesting as a specific graphical language. ST is considered as a basic language because an implementation of a counter machine in IL, FBD/CFC and LD languages is reduced to rewriting blocks of ST-program. The idea of the proof is demonstrated by an example of a Minsky 3-counter machine, which implements a function of squaring.
Keywords: programmable logic controllers (PLC), construction and verification of PLC-programs, LTL-specification, Minsky counter machines. 
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     author = {E. V. Kuzmin and D. A. Ryabukhin and V. A. Sokolov},
     title = {On the expressiveness of the approach to constructing {PLC-programs} by {LTL-specification}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {507--520},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2015_22_4_a4/}
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E. V. Kuzmin; D. A. Ryabukhin; V. A. Sokolov. On the expressiveness of the approach to constructing PLC-programs by LTL-specification. Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 4, pp. 507-520. http://geodesic.mathdoc.fr/item/MAIS_2015_22_4_a4/