Verification of declarative LTL-specification of control programs behavior

The article continues the series of works on development and verification of control programs based on LTL-specifications of a special type. Previously, it was proposed a declarative LTL-specification, which allows describing the behavior of control programs and building program code based on it in the imperative ST-language for programmable logic controllers. The LTL-specification can be directly verified for compliance with specified temporal properties by the model checking method using the nuXmv symbolic verification tool. In general, it is not required translating LTL-formulas of the specification into another formalism — an SMV-specification (code in the input language of the nuXmv tool).
The purpose of this work is to explore alternative ways of representing a program behavior model corresponding to the declarative LTL-specification during its verification within the nuXmv tool.
In the article, we transform the declarative LTL-specification into various SMV-specifications with accompanying changes of formulation of the verification problem, what leads to a significant reduction in time costs when checking temporal properties by using the nuXmv tool. The acceleration of verification is due to the reduction of the state space of a model being verified. The SMV-specifications obtained as a result of the proposed transformations specify identical or bisimulationally equivalent transition systems. It is ensuring the same verification results when replacing one SMV-specification with another.