Alban Ponse

The Syntax and Semantics of μCRL

A simple specification language based on CRL (Common Representation Language)and therefore called μCRL (micro CRL) is proposed. It has been developed to study processes with data. So the language contains only basic constructs with an easy semantics. To obtain executability, effective μCRL has been defined. In effective μCRL equivalence between closed data-terms is decidable and the operational behaviour is finitely branching and computable. This makes effective μCRL a good platform for tooling activities.

Process algebra with iteration and nesting

We introduce iteration in process algebra by means of (the original, binary version of) Kleenes star operation: x * y is the process that chooses between x and y, and upon termination of x has this choice again. We add this operation to a whole range of process algebra axiom systems, starting from BPA (Basic Process Algebra). In the case of the most complex system under consideration, ACP τ , every regular process can be defined with handshaking (two-party communication) and auxiliary actions. Next we introduce nesting in process algebra: x#y is defined by the equation x#y=x(x#y)x+y

Proof Theory for muCRL: A Language for Processes with Data

A simple specification language, called µCRL (micro Common Representation Language), is introduced. It consists of process algebra extended with abstract data types. The language µCRL is designed such that it contains only basic constructs with a straightforward semantics. It has been developed under the assumption that an extensive and mathematically precise study of these constructs and their interaction will yield fundamental insights that are are essential to an analytical approach of well-known and much richer specification languages. To this end, a simple property language is defined in which basic properties of processes, data and the process/data relationship can be expressed in a formal way. Next a proof system is defined for this property language, comprising a rule for induction, the Recursive Specification Principle, and process algebra axioms. The proof theory thus obtained is designed such that automatic proof checking is feasible. It is illustrated with a case study of a counter.

Combining programs and state machines

State machines consume and process actions complementary to programs issuing actions. State machines maintain a state and reply with a boolean response to each action in their interface. As state machines offer a service to programs, their interface is also called a service interface. State machines can be combined with several natural operators, thus giving rise to a state machine calculus. State machines are used for abstract data type modeling.

Execution architectures for program algebra

We investigate the notion of an execution architecture in the setting of the program algebra PGA, and distinguish two sorts of these: analytic architectures, designed for the purpose of explanation and provided with a process-algebraic, compositional semantics, and synthetic architectures, focusing on how a program may be a physical part of an execution architecture. Then we discuss in detail the Turing machine, a well-known example of an analytic architecture. The logical core of the halting problem — the inability to forecast termination behavior of programs — leads us to a few approaches and examples on related issues: forecasters and rational agents. In particular, we consider architectures suitable to run a Newcomb paradox system and the Prisoner’s Dilemma.

Process Algebra with Recursive Operations

Abstract This chapter provides an overview of the addition of various forms of iteration, i.e., recursive operations, to process algebra. Of these operations, (the original, binary version of) the Kleene star is considered most basic, and an equational axiomatisation of its combination with basic process algebra is explained in detail. The focus on iteration in process algebra raised interest in a number of variations of the Kleene star operation, of which an overview, including various completeness and expressivity results, is presented. Though most of these variations concern regular (iterative) operations, also the combination of process algebra and some non-regular operations is discussed, leading to undecidability and stronger expressivity results. Finally, some attention is paid to the interplay between iteration and the special process algebra constants representing the silent step and the empty process.

An introduction to program and thread algebra

We provide an introduction to Program Algebra (PGA, an algebraic approach to the modeling of sequential programming) and to Thread Algebra (TA). PGA is used as a basis for several low- and higher-level programming languages. As an example we consider a simple language with gotos. Threads in TA model the execution of programs. Threads may be composed with services which model (part of) the execution environment, such as a stack. Finally, we discuss briefly the expressiveness of PGA and allude to current work on multithreading and security hazard risk assessment.

Process algebra with guards : combining Hoare logic with process algebra

We extend process algebra with guards, comparable to the guards in guarded commands or conditions in common programming constructs such as ‘if — then — else — fi’ and ‘while — do — od’.The extended language is provided with an operational semantics based on transitions between pairs of a process and a (data-)state. The data-states are given by a data environment that also defines in which data-states guards hold and how atomic actions (non-deterministically) transform these states. The operational semantics is studied modulo strong bisimulation equivalence. For basic process algebra (without operators for parallelism) we present a small axiom system that is complete with respect to a general class of data environments. Given a particular data environmentL we add three axioms to this system, which is then again complete, provided weakest preconditions are expressible andL is sufficiently deterministic.Then we study process algebra with parallelism and guards. A two phase-calculus is provided that makes it possible to prove identities between parallel processes. Also this calculus is complete. In the last section we show that partial correctness formulas can easily be expressed in this setting. We use process algebra with guards to prove the soundness of a Hoare logic for linear processes by translating proofs in Hoare logic into proofs in process algebra.

Division by Zero in Common Meadows

Common meadows are fields expanded with a total multiplicative inverse function. Division by zero produces an additional value denoted with “\({\textup{\textbf{a}}}\)” that propagates through all operations of the meadow signature (this additional value can be interpreted as an error element). We provide a basis theorem for so-called common cancellation meadows of characteristic zero, that is, common meadows of characteristic zero that admit a certain cancellation law.

Kleen's three-valued logic and process algebra

We propose a combination of Kleene’s three-valued logic and ACP process algebra via the guarded commandconstruct. We present an operational semantics in SOS-style, and a completeness result.