An Elementary Proof for Some Semantic Characterizations of Nondeterministic Floyd-Hoare Logic

We give a relatively simple and direct proof for Csirmaz's characterization of Floyd-Hoare logic for nondeterministic programs [5]. (This also yields a very simple proof for Leivant's characterization [13].) We also establish a direct connection between "relational traces" and "time-models" for nondeterministic programs. Introduction In this paper we investigate semantic characterizations of the program verifying power of Floyd-Hoare logic of nondeterministic programs. Our main aim is to obtain a relatively simple and direct proof for Csirmaz's model-theoretic characterization (this is the main theorem of [5]). Furthermore, as a byproduct of Makowsky-Sain [14] and our direct proof for Csirmaz's characterization herein, we get a self-contained and straightforward proof for Leivant's Proposition 9 of [13] (which is a characterization of Floyd-Hoare logic in terms of Henkin-type (or nonstandard) second-order logic): it was shown in [14] that our Corollary 2.1 immediately yields Leivant's characterization, hence our rather easy proof of Corollary 2.1 herein provides an equally easy proof for Leivant's result by [14]. To find simpler proofs (and direct constructions) for Csirmaz's important characterization is a problem which goes back to 1980. A characterization for deterministic programs was found in early 1980 (see [7]) and a stronger char*This project has been supported by the Hungarian National Foundation for Scientific Research, grant no. 1810. The final version of the present paper was completed when I was visiting at Iowa State University, Department of Mathematics, in September 1987. I am grateful to L. Csirmaz for suggestions that considerably improved the mathematical content of this paper. I also wish to express my thanks to A. Pasztor for carefully reading this paper and for her valuable remarks. Received November 20, 1985; revised October 15, 1987