A transformational methodology is described for simultaneously designing algorithms and developing programs. The methodology makes use of three transformational tools - dominated convergence, finite differencing, and real-time simulation of a set machine on a RAM. We illustrate the methodology to design a new O(mn + n 2 )-time algorithm for deciding when n-state, m-transition processes are ready similar, which is a substantial improvement on the \Theta(mn 6 ) algorithm presented in [6]. The methodology is also used to derive a program whose performance, we believe, is competitive with the most efficient hand-crafted implementation of our algorithm. Ready simulation is the finest fully abstract notion of process equivalence in the CCS setting. 1 Introduction Currently there is a wide gap between the goals and practices of research in the theory of algorithm design and the science of programming, which we believe is A preliminary version of this paper appeared in the Conf...

We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions

) Frits W. Vaandrager MIT Laboratory for Computer Science Cambridge, MA 02139, USA frits@theory.lcs.mit.edu Abstract The relation between process algebra and I/O automata models is investigated in a general setting of structured operational semantics (SOS). For a series of (approximations of) key properties of I/O automata, syntactic constraints on inference rules are proposed which guarantee these properties. A first result is that, in a setting without assumptions about actions, the well-known trace and failure preorders are substitutive for any set of rules in a format due to De Simone. Next additional constraints are imposed which capture the notion of internal actions and guarantee substitutivity of the testing preorders of De Nicola and Hennessy, and also of a preorder related to the failure semantics with fair abstraction of unstable divergence of Bergstra, Klop and Olderog. Subsequent constraints guarantee that input actions are always enabled and output actions cannot be bl...

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In this paper we describe the promoted tyft/tyxt rule format for defining higher-order languages. The rule format is a generalization of Groote and Vaandrager 's tyft/tyxt format in which terms are allowed as labels on transitions in rules. We prove that bisimulation is a congruence for any language defined in promoted tyft/tyxt format and demonstrate the usefulness of the rule format by presenting promoted tyft/tyxt definitions for the lazy -calculus, CHOCS and the ß-calculus. 1 Introduction For a programming language definition that uses bisimulation as the notion of equivalence, it is desirable for the bisimulation relation to be compatible with the language constructs; i.e. that bisimulation be a congruence. Several rule formats have been defined, so that as long as a definition satisfies certain syntactic constraints, then the defined bisimulation relation is guaranteed to be a congruence. However these rule formats have not been widely used for defining languages with higher-...

In a similar way as 2-categories can be regarded as a special case of double categories, rewriting logic (in the unconditional case) can be embedded into the more general tile logic, where also side-effects and rewriting synchronization are considered. Since rewriting logic is the semantic basis of several language implementation efforts, it is useful to map tile logic back into rewriting logic in a conservative way, to obtain executable specifications of tile systems. We extend the results of earlier work by two of the authors, focusing on some interesting cases where the mathematical structures representing configurations (i.e., states) and effects (i.e., observable actions) are very similar, in the sense that they have in common some auxiliary structure (e.g., for tupling, projecting, etc.). In particular, we give in full detail the descriptions of two such cases where (net) process-like and usual term structures are employed. Corresponding to these two cases, we introduce two ca...

We set up a formal framework to describe transition system specifications in the style of Plotkin. This framework has the power to express many-sortedness, general binding mechanisms and substitutions, among other notions such as negative hypotheses and unary predicates on terms. The framework is used to present a conservativity format in operational semantics, which states sufficient criteria to ensure that the extension of a transition system specification with new transition rules does not affect the semantics of the original terms.

The computational engine of the verification tool UPPAAL consists of a collection of efficient algorithms for the analysis of reachability properties of systems. Model-checking of properties other than plain reachability ones may currently be carried out in such a tool as follows. Given a property to model-check, the user must provide a test automaton T for it. This test automaton must be such that the original system S has the property expressed by precisely when none of the distinguished reject states of T can be reached in the parallel composition of S with T . This raises the question of which properties may be analyzed by UPPAAL in such a way. This paper gives an answer to this question by providing a complete characterization of the class of properties for which model-checking can be reduced to reachability testing in the sense outlined above. This result is obtained as a corollary of a stronger statement pertaining to the compositionality of the property language considered in this study. In particular, it is shown that our language is the least expressive compositional language that can express a simple safety property stating that no reject state can ever be reached. Finally, the property language characterizing the power of reachability testing is used to provide a definition of characteristic properties with respect to a timed version of the ready simulation preorder, for nodes of -free, deterministic timed automata.

Fokkink and Zantema ((1994) Computer Journal 37:259–267) have shown that bisimulation equivalence has a finite equational axiomatization over the language of Basic Process Algebra with the binary Kleene star operation (BPA ∗). In the light of this positive result on the mathematical tractability of bisimulation equivalence over BPA ∗ , a natural question to ask is whether any other (pre)congruence relation in van Glabbeek’s linear time/branching time spectrum is finitely (in)equationally axiomatizable over it. In this paper, we prove that, unlike bisimulation equivalence, none of the preorders and equivalences in van Glabbeek’s linear time/branching time spectrum, whose discriminating power lies in between that of ready simulation and that of completed traces, has a finite equational axiomatization. This we achieve by exhibiting a family of (in)equivalences that holds in ready simulation semantics, the finest semantics that we consider, whose instances cannot all be proven by means of any finite set of (in)equations

In this paper we present history-dependent automata (HD-automata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with history-dependent formalisms. In a history-dependent formalism the actions that a system can perform carry information generated in the past history of the system. The most interesting example is -calculus: channel names can be created by some actions and they can then be referenced by successive actions. Other examples are CCS with localities and the history-preserving semantics of Petri nets. Ordinary