Inge Bethke

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

A propositional logic with four values : true, false, divergent and meaningless

ABSTRACT In this paper, we survey 3-valued logics and their complete axiomatizations, one of which may be new. We then propose a 4-valued, functionally complete logic that incorporates these 3-valued systems and provide notations for interesting operators and subsystems.

An upper bound for the equational specification of finite state services

The communication mechanism between client and server tasks can be modeled by a simple rendezvous model. The intuition here is that a process— the client—when executed places its requests into a request buffer. These requests are taken from the buffer by another process—the server. After some processing, prescribed by actions of the server, the server returns a Boolean reply indicating success or failure of the request. In this note—which is an adaptation of a contribution to the Liber Amicorum in honor of the 50th birthday of John-Jules Meyer- we shall describe the algebra of state services which corresponds to the server side of the communication model.

Decision problems for pushdown threads

Threads as contained in a thread algebra emerge from the behavioral abstraction from programs in an appropriate program algebra. Threads may make use of services such as stacks, and a thread using a single stack is called a pushdown thread. Equivalence of pushdown threads is shown decidable whereas pushdown thread inclusion is undecidable. This is again an example of a borderline crossing where the equivalence problem is decidable, whereas the inclusion problem is not.

Equations for formally real meadows

We consider the signatures Σ m = ( 0 , 1 , - , + , ? , - 1 ) of meadows and ( Σ m , s ) of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom scheme expressing formal realness; the second axiomatization presupposes an ordering. We apply these completeness results in order to obtain complete axiomatizations of the complex numbers.

Thread algebra and risk assessment services

Threads as contained in a thread algebra emerge from the behavioral abstraction from programs in an appropriate program algebra. Threads may makeion from programs in an appropriate program algebra. Threads may make use of services such as stacks, and a thread using a single stack is called a pushdown thread. Equivalence of pushdown threads is decidable. Using this decidability result, an alternative to Cohen’s impossibility result on virus detection is discussed and some results on risk assessment services are proved. §

Predictable and Reliable Program Code: Virtual Machine-based Projection Semantics

Publisher Summary This chapter presents a simple theory developing a reliable syntax, whose execution semantics are unambiguous. Of all the languages used by system administrators and operators in deploying services (e.g. PHP, Perl, TCL, Scheme, etc.) few can be said to have such a clear connection between syntax and behavior. The system world would do well to foster this kind of predictability in future technologies. Today there is a need for a new generation of languages for system management, in a variety of contexts. One example is configuration management. Configuration management is currently an active area. The chapter highlights the role of layers of language abstraction and their effect on semantics of language statements and shows how these languages can be built up from low-level primitives through virtualiation layers to high-level constructs, so that we might build new languages that are “correct by construction”. A simple program notation for object oriented programming has been provided admitting a projection semantics. Many more features exist and the project of syntax design has only been touched upon. Still the claim is made that the above considerations provide a basis for the design of reliable syntax for much more involved program notations. Projection semantics provides a scientifically well-founded and rigorous, yet simple approach to the semantics of programming languages. Future work will have to clarify that this framework is industrially viable for the high-level design and analysis of complex systems, and for natural refinements of models to executable and reliable code.

The structure of finite meadows

A meadow is a commutative ring with a total inverse operator satisfying 0−1=0. We show that the class of finite meadows is the closure of the class of Galois fields under finite products. As a corollary, we obtain a unique representation of minimal finite meadows in terms of finite prime fields.

Note on paraconsistency and reasoning about fractions

We apply a paraconsistent strategy to reasoning about fractions.

On the Contribution of Backward Jumps to Instruction Sequence Expressiveness

We investigate the expressiveness of backward jumps in a frame work of formalized sequential programming called program algebra and characterize established non-uniform complexity classes in terms of instruction sequences, backward jumps and auxiliary registers.