Yuxi Fu

A Proof Theoretical Approach to Communication

The paper investigates a concurrent computation model, chi calculus, in which communications resemble cut eliminations for classical proofs. The algebraic properties of the model are studied. Its relationship to sequential computation is illustrated by showing that it incorporates the operational semantics of the call-by-name lambda calculus. Practically the model has pi calculus as a submodel.

On the expressiveness of interaction

Subbisimilarity is proposed as a general tool to classify the relative expressive power of process calculi. The expressiveness of several variants of CCS is compared in terms of the subbisimilarity relationship. Similar investigation is also carried out for the variants of the pi calculus. The relative expressiveness of the different forms of the choice operation and the different ways of introducing infinite behaviors are systematically studied in both the frameworks of CCS and pi. Some issues concerning the expressiveness of both CCS and pi are clarified. Several open problems are solved along the way. The subbisimilarity approach and the relative expressiveness results are applied to show the independence of the operators of the pi calculus. The definition of the subbisimilarity relationship can be further strengthened with computational requirement, leading to a uniform treatment of computation and interaction.

Theory of Interaction

Abstract Theory of Interaction aims to provide a foundational framework for computation and interaction. It proposes four fundamental principles that characterize the common features of all models of computation and interaction. These principles suffice to support a model independent treatment of the two most important relationships in computer science, the equality between processes and the relative expressiveness between models. Based on the two relationships the theory of equality, the theory of expressiveness and the theory of completeness are developed.

Error Estimation of Perturbations Under CRI

The analysis of stability and robustness of fuzzy reasoning is an important issue in areas like intelligent systems and fuzzy control. An interesting aspect is to what extent the perturbation of input in a fuzzy reasoning scheme causes the oscillation of the output. In particular, when the error limits (restrictions) of the input values are given, what the error limits of the output values are. In this correspondence, we estimate the upper and lower bounds of the output error affected by the perturbation parameters of the input, and obtain the limits of the output values when the input values range over some interval in many fuzzy reasoning schemes under compositional rule of fuzzy inference (CRI)

Tau laws for pi calculus

The paper investigates the nonsymbolic algebraic semantics of the weak bisimulation congruences on finite pi processes. The weak bisimulation congruences are studied both in the absence and in the presence of the mismatch operator. Some interesting phenomena about the open congruences are revealed. Several new tau laws are discovered and their relationship is discussed. The contributions of the paper are mainly as follows: 1. It is proved that Milners three tau laws fail to lift a complete system for the strong open congruence to a complete system for the weak open congruence in the absence of both the mismatch operator and the restriction operator. A fourth tau law is proposed to deal with the match operator under the prefix operation. It is shown that for this calculus a complete system for the strong open congruence extended with all the four tau laws is complete for the weak open congruence. 2. It is verified that the four tau laws are also enough for the weak open congruence of the pi calculus without the mismatch operator. A complete system using distinctions is given. 3. It is pointed out that the standard definition of the weak open congruence gives rise to a bad equivalence relation in the presence of the mismatch operator. Two alternatives are proposed. These are the late open congruence and the early open congruence. Their difference is similar to that between the weak late congruence and the weak early congruence. Complete axiomatic systems for the two weak open congruences are given.

On quasi-open bisimulation

Quasi-open bisimilarity is a variant of the open bisimilarity based on a closer examination of the observationality of local names. The paper investigates two alternative characterizations of the quasi-open bisimilarity and provides a complete system for the weak quasi-open congruence.

Bisimulation Lattice of Chi Processes

Chi calculus was proposed as a process algebra that has a uniform treatment of names. The paper carries out a systematic study of bisimilarities for chi processes. The notion of L-bisimilarity is introduced to give a possible classification of bisimilarities on chi processes. It is shown that the set of L-bisimilarities forms a four element lattice and that well-known bisimilarities for chi processes fit into the lattice hierarchy. The four distinct L-bisimilarities give rise to four congruence relations. Complete axiomatization system is given for each of the four relations. The bisimulation lattice of asynchronous chi processes and that of asymmetric chi processes are also investigated. It turns out that the former consists of two elements while the latter twelve elements. Finally it is pointed out that the asynchronous asymmetric chi calculus has a bisimulation lattice of eight elements.

Chi Calculus with Mismatch

The theory of chi processes with the mismatch operator is studied. Two open congruence relations are investigated. These are weak early open congruence and weak late open congruence. Complete systems are given for both congruence relations. These systems use some new tau laws. The results of this paper correct some popular mistakes in literature.

Checking equality and regularity for normed BPA with silent moves

The decidability of weak bisimilarity on normed BPA is a long standing open problem. It is proved in this paper that branching bisimilarity, a standard refinement of weak bisimilarity, is decidable for normed BPA and that the associated regularity problem is also decidable.

The λ-calculus in the π-calculus

A general approach is proposed that transforms, in the framework of pi calculus, objects to methods in an on-the-fly manner. The power of the approach is demonstrated by applying it to generate an encoding of the full lambda calculus in the pi calculus. The encoding is proved to preserve and reflect beta reduction and is shown to be fully abstract with respect to Abramsky’s applicative bisimilarity.