A proof tableau of Hoare logic is an annotated program with preand post-conditions, which corresponds to an inference tree of Hoare logic. In this paper, we show that a proof tableau for partial correctness can be transformed into an inference sequence of rewriting induction for constrained rewriting. We also show that the resulting sequence is a valid proof for an inductive theorem correspondi...

We define Concurrent Turing Machines (CTMs) as Turing machines with Petri nets as finite control. This leads to machines with arbitrary many tape heads, thus subsuming any class of (constant) khead Turing machines. Concurrent Turing machines correspond to a class of multiset rewriting systems. The definition of a CTMs as a rewrite theory avoids the need for encoding multisets as words and using...

Currently, the paradigm of algebraic programming becomes one of the most important paradigms of declarative programming. Algebraic programming is based on methods of term rewriting [1], which are widely used independently and in programming systems based on other paradigms (in functional, logical, object-oriented, and agent-based programming, in computer algebra and systems of theorem proving)....

Combining symbolic techniques such as: (i) SMT solving, (ii) rewriting modulo theories, and (iii) model checking can enable the analysis of infinite-state systems outside the scope of each such technique. This paper proposes rewriting modulo SMT as a new technique combining the powers of (i)-(iii) and ideally suited to model and analyze infinite-state open systems; that is, systems that interac...

We present a term rewriting system for interval arithmetic (addition, subtraction and multiplication), toward a mathematical model for interval computation. We start presenting a term rewriting system whose rules (directed equations) perform binary floating-point arithmetic, which is based on IEEE-754 Standard. Next, this primitive system is extended with rules for interval arithmetic. Finally,...

In this paper, we present a high-level formalism based on port graph rewriting, strategic rewriting, and rewriting calculus. We show that this formalism is suitable for modeling autonomic systems and we illustrate its expressivity for modeling properties of such systems using an example of a mail delivery system.

Context-sensitive rewriting is a restriction of term rewriting used to model evaluation strategies in functional programming and in programming languages like OBJ. For example, under certain conditions termination of an OBJ program is equivalent to innermost termination of the corresponding contextsensitive rewrite system [25]. To prove termination of context-sensitive rewriting, several method...

Generalizing results of Otto & Ruškuc, this paper shows that every finitely generated submonoid of a monoid presented by a confluent finite special rewriting system admits an automatic structure that is simultaneously rr-, `r-, r`-, and ``-automatic; and that every finitely generated submonoid of a monoid presented by a confluent regular monadic rewriting system admits an automatic structure th...