Articles
An approach to the construction and verification of PLC IL-programs for discrete problems is proposed. For the specification of the program behavior, we use the linear-time temporal logic LTL. Programming is carried out in the IL-language (Instruction List) according to an LTL-specification. The correctness analysis of an LTL-specification is carried out by the symbolic model checking tool Cadence SMV. A new approach to programming and verification of PLC IL-programs is shown by an example. For a discrete problem, we give an IL-program and its LTL-specification.
The purpose of the article is to describe an approach to programming PLC, which would provide a possibility of IL-program correctness analysis by the model checking method.
Under the proposed approach, the change of the value of each program variable is described by a pair of LTL-formulas. The first LTL-formula describes situations which increase the value of the corresponding variable, the second LTL-formula specifies conditions leading to a decrease of the variable value. The LTL-formulas (used for speci- fication of the corresponding variable behavior) are constructive in the sense that they construct the PLC-program (IL-program), which satisfies temporal properties expressed by these formulas. Thus, the programming of PLC is reduced to the construction of LTLspecification of the behavior of each program variable. In addition, an SMV-model of a PLC IL-program is constructed according to LTL-specification. Then, the SMV-model is analysed by the symbolic model checking tool Cadence SMV.
Algebraic program models with procedures are designed to analyze program semantic properties on their models called program schemes. Liberisation and equivalence problems are stated for program models with procedures. A subclass of program models with procedures called special gateway models is investigated. A better complexity algorithm for the liberisation in such models is proposed. Primitive program schemes are defined as a subclass of special gateway models. It is shown that the equivalence problem in such models is decidable if the equivalence problem is decidable in special program models without procedures. For some cases of decidability the complexity is evaluated.
A modification of the well-known FitzHugh–Nagumo model from neuroscience is proposed. This model is a singularly perturbed system of ordinary differential equations with a fast variable and a slow one. The existence and stability of a nonclassical relaxation cycle in this system are studied. The slow component of the cycle is asymptotically close to a discontinuous function, while the fast component is a δ-like function. A onedimensional circle of unidirectionally coupled neurons is considered. It is shown the existence of an arbitrarily large number of traveling waves for this chain. In order to illustrate the increasing of the number of stable traveling waves numerical methods were involved.
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