Some general incompleteness results for partial correctness logics

AbstractIt is known that incompleteness of Hoare's logic relative to certain data type specifications can occur due to the ability of partial correctness assertions to code unsolvable problems; cf. Andréka, Németi, and Sain (1979, Lecture Notes in Computer Science Vol. 74, pp. 208–218, Springer-Verlag, New York/Berlin) and Bergstra and Tucker (1982, Theoret. Comput. Sci. 17, 303–315). We improve what we think are the main known theorems of this kind, showing that they depend only on very weak assumptions on the data type specification (ensuring the ability to simulate arbitrarily long finite initial segments of the natural numbers with successor), and pointing out that the recursion theoretic strength of the obtained results can be increased

Proving Properties of Real-Time Distributed Systems: A Comparison of Three Approaches

Three formal methods for specifying properties of real-time systems are reviewed and used in a common example. Two of them offer a graphical representation and the third is an algebraic language. The example is that of an automatic railroad system with sensors to detect the train position and controls for the gate mechanism. Associated with each formalism is a proof methodology which is described and used to prove a safety property about the example. A comparison is made between the three formalisms according to various criteria including the expressiveness, readability, maintainability of the language, support for real-time concepts, method for expressing properties and proof mechanisms