Hardness of preorder checking for basic formalisms

Hardness of Preorder Checking for Basic Formalisms

We investigate the complexity of preorder checking when the specification is a flat finite-state system whereas the implementation is either a non-flat finite-state system or a standard timed automaton. In both cases, we show that simulation checking is EXPTIME-hard, and for the case of a non-flat implementation, the result holds even if there is no synchronization between the parallel componen...

Some Basic Formalisms in Numerical Variational Analysis

This study aims at the theoretical development of a method of “four-dimensional analysis,” namcly the numerical variational analysis. The three basic types of variational formalism in the nurncrical variational analysis method are discussed. The basic formalisms are categorized into three areas: (1) “timewise localized” formalism, ( 2 ) formalism with strong constraint, and (3) formalism with w...

From Basic Views and Aspects to Integration of Specification Formalisms

Probabilistic Checking of Proofs and Hardness of Approximation Problems

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Probabilistic Checking of Proofs and Hardness of Approximation

This paper introduces basic notions of classic computational complexity theory and probabilistically checkable proof. It sketches the proof of the PCP theorem, and discusses its applications to the hardness of approximation of various problems.