## IFIP Working Group 2.2 Meeting 25 - 29 September 2000, Oldenburg, Germany.

### Davide Sangiorgi (joint work with Francesca Levi) Controlling Interference in Ambients

Two forms of interferences are individuated in Cardelli and Gordon's Mobile Ambients (MA): plain interferences, which are similar to the interferences one finds in CCS and pi-calculus; and grave interferences, which are more dangerous and may be regarded as programming errors. To control interferences, the MA movement primitives are modified. On the new calculus, the Safe Ambients (SA), a type system is defined that: controls the mobility of ambients; removes all grave interferences. Other advantages of SA are: a useful algebraic theory; programs sometimes more robust (they require milder conditions for correctness) and/or simpler. These points are illustrated on several examples.

The talk is based on joint work with Francesca Levi (University of Pisa), published in the proceedings of POPL'00.

### Wojciech Penczek Efficient methods for model checking of Timed Petri Nets

Model checking is one of the most popular methods of automated verification of concurrent systems, e.g., hardware circuits, communication protocols, and distributed programs. However, the practical applicability of this method is strongly restricted by the state explosion problem, which is mainly caused by representing concurrency of operations by their interleaving. Therefore, many different reduction techniques have been introduced in order to alleviate the state explosion. The major methods include application of partial order reductions, symmetry reductions, abstraction techniques, BDD-based symbolic storage, and SAT-related algorithms. Recently, the interest in automated verification is moving towards concurrent real-time systems. Two main models for representing such systems are usually exploited: timed automata and Time Petri Nets. The properties to be verified are expressed in either a standard temporal logic like LTL and CTLS, or in its timed versions like LTL$_\Delta$, MITL, and TCTL. The lecture is on verification of timed and untimed branching time temporal properties of Time Petri Nets. Since Time Petri Nets have usually infinite state spaces, abstraction techniques are used to represent these by finite ones. To reduce the sizes of abstract state spaces partial order reductions are exploited. In this lecture an automata-theoretic approach to model-checking is applied. The theoretical framework developed by Kupferman-Vardi-Wolper is used, where it is shown that the problem of branching-time model checking can be translated to checking the non-emptiness of an alternating 1-letter word automaton. The latter problem is known to have a linear complexity, which allows to perform verification efficiently. The outline of the lecture is as follows:
• Introduction to model checking - automata-theoretic approach,
• Reduction methods for untimed global state approaches: on-the-fly, po-reductions, symbolic (BDDs), translation to SAT,
• Timed and untimed temporal logics: LTL, CTLS, ACTLS, LTL$_\Delta$, MITL, and TCTL,
• Translations from temporal logics to automata,
• Timed Petri Nets,
• Abstractions preserving timed and untimed temporal logics,
• Partial order reductions for Time Petr Nets.
The main novelty of the presented work relies on:
• improving the variant of the geometric region method for defining abstract state spaces preserving properties of \CTLS\/ and \ACTLS\/ such that the structure of a verified formula is exploited,
• showing how to extend the po-reduction methods to deal with branching properties of Time Petri Nets.
The lecture is based on the following papers of the author:
• W. Penczek: Partial order reductions for checking branching properties of Timed Petri Nets, Proc. of CS\&P, Berlin, to appear, 2000.
• W. Penczek, M. Szreter, R. Gerth and R. Kuiper: Improving Partial Order Reductions for Universal Branching Timed Properties, Fundamenta Informaticae, to appear, 2000.
• M. Szreter and W. Penczek: More than one, less than all: Linear to Branching revisited, Proc. of CS\&P, Berlin, to appear, 2000.
• R. Gerth, R. Kuiper, D. Peled, and W. Penczek: A Partial Order Approach to Branching Time Logic Model Checking, Information and Computation, Vol. 150, No. 2, pp. 132-152, 1999.

### Igor Walukiewicz Deciding low levels of the mu-calculus alternation hierarchy

Consider the hierarchy obtained by alternating least and greatest fixpoints in mu-calculus terms. Alternatively this hierarchy can be characterised by sizes of winning conditions in automata on trees. The problem is: "given a regular tree language establish the least number of fixpoint alternations needed to write a term defining the language".

I will show that it is EXPTIME-complete to decide if the language can be written using the least fixpoints only. The same bound also holds for terms with only the greatest fixpoints. The case of mixed (but not alternating) fixpoints is already much more difficult to solve. The subject is also a good occasion to give a very short summary of what is known about the alternation hierarchy.

### Georghe Stefanescu Using space-time duality to structure interaction systems

Space-time duality may by used to transform simple imperative programs into (pure) object-oriented programs. By this mechanism the usual memory states describing (spatial) interfaces of imperative programs are transformed into temporal interfaces of interacting systems. As a side-effect, this suggest a way to pass from the current stream-based temporal interfaces to abstract, highly structured temporal interfaces. In the same time, the well-known techniques used for structured programms in imperative programming area may be used to obtain structural interaction systems. Finaly, but clearly a very important point, the classical program verification techniques for imerative programms may be used to get similar tools for object-orineted programs.

The aim of the talk is to present the space-time duality mechanism and to look at a few aspects of the interaction systems which have to be reconsidered in the view of space-time duality. Also, a few technical ingredients, most of them based on the network algebra approach, will be presented.

For more on this, one may have a look on the book: G. Stefanescu, Network Algebra, Springer-Verlag, London/Berlin/... http://funinf.cs.unibuc.ro/~ghstef/na/myAdv.html

### Hans Langmaack (work with M. Mueller-Olm and A. Wolff) On preservation of relative correctness

M. Mueller-Olm and A. Wolf have introduced the notions relative correctness of programs'' and preservation of relative correctness of program implementations and of compilations''. These notions generalize the notions of total resp. partial correctness and their preservations. The latter notions do not satisfy enough the requirements in practical software engineering and program compilation. Realistic software implementation and compiler construction have to master in the same context both types of errors: of acceptable, excusable, unavoidable errors on the one hand and of unacceptable, inexcusable, avoidable ones on the other.

It is quite known that total program correctness is more difficult to prove than partial correctness. But it is most interesting to see that for preservation of total resp. partial correctness the situation is the other way round. This phenomenon has been first observed when compiling while-programs into flat assembly code with unconditional and conditional jumps [MOl95] and later when translating ALGOL-like programs with nested blocks, parameterless procedures and static scoping into flat assembly code augmented by subroutine and return jumps [MOW00,Wol00]. Source languages are assumed to be furnished with denotational (predicate transformer) semantics, target languages with operational step semantics.

The decisive difference is evoked by the premis whether divergence (infinite computation) is considered to be an unacceptable error (generalized total correctness) or to be an acceptable one (generalized partial correctness). The inductive proof of generalized total correctness preservation utilizers just a series of algebraic laws for assembly instructions semantics. But above that, proof of preservation of generalized partial correctness has to exploit a fixpoint characterization of the operational target semantics. In case divergence is unacceptable operational target semantics is indeed the least fixpoint of a certain functional, otherwise the largest fixpoint [MOl97,MOW99,MOW00,Wol00].

Easiness of proof might be an indication why software engineering in the past has favoured preservation of total correctness for software implementation. But in usual information processing outside process programming preservation of (generalized) partial correctness is at least as important, especially because realistic target machines with their finite resources cannot fulfill all total program correctness wishes.

Most realistic compilers do a lot of code optimizations like dead or redundant code elimination, code motion or unswitching. But often language and compiler manuals do not inform the users decently enough about correctness of optimizations, namely what conditions source programs must fulfill and what consequences on computing results are to be expected. Relative program correctness and its preservartion allow very precise investigations and delineations of these conditions and consequences [MOW99,MOW00,Wol00].

[MOl95]
M. Mueller-Olm. An Exercise in Compiler Verification. Kiel, 1995. Available from the author.
[MOl97]
M. Mueller-Olm. Modular Compiler Verification: A Refinement-Algebraic Approach Advocating Stepwise Abstraction. LNCS, Vol. 1283, Springer-Verlag, 1997.
[MOW99]
M. Mueller-Olm and A. Wolf. On Excusable and Inexcusable Failures: On an Adequate Notion of Translation Correctness. In J. Wing, J. Woodcock and J. Davies (eds.), FM '99 - Formal Methods. LNCS, vol. 1709, 1107 - 1127, Springer-Verlag, 1999.
[MOW00]
M. Mueller-Olm and A. Wolf. On the Translation of Procedures to Finite Machines: Abstraction allows a Clean Proof. In G. Smolka (ed.) Programming Languages and Systems. Proc. ESOP 2000, LNCS, vol. 1782, 290 - 304, Springer-Verlag, 2000.
[Wol00]
A. Wolf. Weakest Relative Precondition Semantics: Balancing Approved Theory and Realistic Translation Verification. Univ. Kiel, dissertation, subm. 2000.

abstract

### Catuscia Palamidessi Probabilistic asynchronous $\pi$-calculus

We propose an extension of the asynchronous $\pi$-calculus with a notion of random choice. We define an operational semantics which distinguishes between probabilistic choice, made internally by the process, and nondeterministic choice, made externally by an adversary scheduler. This distinction will allow us to reason about the probabilistic correctness of algorithms under certain schedulers. We show that in this language we can solve the electoral problem, which was proved not possible in the asynchronous $\pi$-calculus. Finally, we show an implementation of the probabilistic asynchronous $\pi$-calculus in a Java-like language.

### Philippe Darondeau (joint work with B.Caillaud, L.Helouet, and G.Lesventes) Realizing HMSC's by Distributable PN's

High Level Message Sequence Charts (HMSC's) may be considered as specifications for distributed systems. Realization thereof may be seeked in distributable Petri nets, a subclass of Petri nets where transitions are endowed with locations and conflicts between transitions are always local. Distributable nets translate actually to equivalent (up to branching bisimulation) families of automata communicating by asynchronous messages. One can unfortunately not decide whether a given HMSC may be realized exactly (i.e. up to the equality of languages) by some distributable Petri net. We advocate therefore for taking HMSC's as incomplete specifications. In this case, each HMSC has an optimal realization by a distributable Petri net, with the least language including the language of the HMSC. This realization may be computed and it may also be model-checked. We set the question whether relations between specifications and realizations of reactive systems should not be reconsidered in this way.

### Masahiko Sato $\alpha$: A purely functional language with imperative language inside

We present a purely functional language $\alpha$ that naturally contains an imperative language as its sublanguage. $\alpha$ is pure in the sense that (1) it is confulent and (2) it is a conservative extension of the pure $\lambda$ calculus. The purity of $\alpha$ makes it a mathematically and logically well founded language. For example, it becomes possible to prove properties of programs written in $\alpha$ by equational reasoning.

The main characteristic of $\alpha$ is that it has environments as first-class objects. By using first-class environments, we can encapsulate imperative programs by treating imperative programs as environment tranformers. In this way, side-effects caused by the execution of imperative programs becomes invisible from outside.

We also discuss another usages of first-class environments. For example, we show that given an abstract obtained by abstracting several variables, we can instantiate any of these variables by specifying the name of the variable to be instantiated and the value which will replace the variable.

WG 2.2 (darondeau@irisa.fr)