Team VASY

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Section: New Results

Models and Verification Techniques

The CÆSAR_SOLVE Library

Participant : Radu Mateescu.

Cæsar_Solve is a generic software library for solving boolean equation systems of alternation depth 1 (i.e., without mutual recursion between minimal and maximal fixed point equations) on the fly. This library is at the core of several Cadp verification tools, namely the equivalence checker Bisimulator (see §  6.1.2 ), the model checker Evaluator  3.5 (see §  6.1.3 ), and the minimization tool Reductor  5.0 (see §  6.1.4 ). The resolution method is based on boolean graphs, which provide an intuitive representation of dependencies between boolean variables, and which are handled implicitly, in a way similar to the Open/Cæsar interface [3] .

The Cæsar_Solve library provides five different resolution algorithms. A1 and A2 are general algorithms based upon depth-first, respectively breadth-first, traversals of boolean graphs. A3 and A4, based upon memory-efficient depth-first traversals of boolean graphs, are optimized for the case of acyclic, respectively disjunctive/conjunctive, boolean graphs. A5 is a general algorithm based upon a depth-first traversal of boolean graphs; it generalizes Tarjan's algorithm for computing strongly connected components and is much faster than A1 and A2 when it is invoked many times on the same equation block. All these algorithms can generate diagnostics explaining why a result is true or false (examples and counterexamples).

In 2006, the Cæsar_Solve library (12, 200 lines of C code) was improved as follows:

An article about Cæsar_Solve was published in an international journal [22] .

The BISIMULATOR Tool

Participant : Radu Mateescu.

Bisimulator is an equivalence checker that takes as input two graphs to be compared (one represented implicitly using the Open/Cæsar environment, the other represented explicitly as a Bcg file) and determines whether they are equivalent (modulo a given equivalence relation) or whether one of them is included in the other (modulo a given preorder relation). Bisimulator works on the fly, meaning that only those parts of the implicit graph pertinent to verification are explored. Due to the use of Open/Cæsar , Bisimulator can be applied directly to descriptions written in high level languages (for instance, Lotos ). This is a significant improvement compared to older tools (such as Aldébaran and Fc2Implicit ) which only accepted lower level models (networks of communicating automata).

Bisimulator works by reformulating the graph comparison problem in terms of a boolean equation system, which is solved on the fly using the Cæsar_Solve library (see §  6.1.1 ). A useful functionality of Bisimulator is the generation of a ``negative'' diagnostic (i.e., a counterexample), which explains why two graphs are not equivalent (or not included one in the other). The diagnostics generated by Bisimulator are directed acyclic graphs and are usually much smaller than those generated by other tools (such as Aldébaran ) that can only generate counterexamples restricted to sets of traces.

In 2006, we continued the development of Bisimulator (15, 900 lines of C code). In addition to a bug fix related to the counterexample generation for branching equivalence:

The EVALUATOR Tool

Participants : Radu Mateescu, Damien Thivolle.

Evaluator is a model checker that evaluates a temporal logic property on a graph represented implicitly using the Open/Cæsar environment. Properties are described in regular alternation-free $ \mu$ -calculus, a logic built from boolean operators, possibility and necessity modalities containing regular expressions denoting transition sequences, and fixed point operators without mutual recursion between least and greatest fixed points. The input language of the tool also allows to define parameterized temporal operators and to group them into separate libraries.

Evaluator works on the fly, meaning that only those parts of the implicit graph pertinent to verification are explored. The model checking problem is reformulated in terms of solving a boolean equation system. A useful feature of Evaluator is the generation of diagnostics (examples and counterexamples) explaining why a formula is true or false.

In 2006, we continued the development of the Evaluator  3.5 tool. In particular, the translation in regular alternation-free $ \mu$ -calculus of the inevitability operator of Actl was improved. When using Evaluator  3.5 to check temporal formulas containing this operator, the new translation leads to gains in time and memory up to a factor 8.

We also continued our work (undertaken in 2003) for extending the regular alternation-free $ \mu$ -calculus with new operators dedicated to the specification of properties involving data values. This led to a prototype Evaluator  4.0 (37, 600 lines of Syntax /Lotos NT code and 11, 100 lines of C code), which brings the following enhancements with respect to Evaluator  3.5:

The prototype version Evaluator  4.0 was successfully tested on 2, 300 examples of Mcl formulas and on all regular alternation-free $ \mu$ -calculus formulas available in the demo examples of the Cadp distribution.

The REDUCTOR and DETERMINATOR Tools

Participants : Frédéric Lang, Radu Mateescu.

The Reductor  4.0 tool of Cadp , developed in 2005, implements several forms of (partial or total) graph reductions. Some of these reductions are obtained by encoding the reduction problem into a boolean equation system that is solved on the fly using the Cæsar_Solve library (see §  6.1.1 ).

Cadp also contains a tool named Determinator , which eliminates nondeterminism from ordinary or stochastic graphs.

In 2006, we released a new version 5.0 of Reductor , together with a new version of Determinator . Reductor  5.0 includes several functionalities previously available in Determinator . The main changes are the following:

Compositional Verification Tools

Participants : Hubert Garavel, Frédéric Lang.

The Cadp toolbox contains various tools dedicated to compositional verification, among which Projector  2.0, Exp.open  2.0, and Svl play a central role.

Projector  2.0 implements behavior abstraction [56] , [61] by taking into account interface constraints.

Exp.open  2.0 explores on the fly the graph corresponding to a network of communicating automata (represented as a set of Bcg files).

Svl (Script Verification Language ) is both a high level language for expressing complex verification scenarios and a compiler dedicated to this language.

In 2006, we enhanced these tools along the following lines:

An article on refined interface generation using Exp.open and Svl (see the Vasy  2005 activity report) was published in an international conference [29] .

Parallel and Distributed Verification Tools

Participants : Jérôme Fereyre, Hubert Garavel, Radu Mateescu.

Enumerative verification algorithms need to explore and store very large graphs and, thus, are often limited by the capabilities of one single sequential machine. To push forward the limits, we are studying parallel and distributed algorithms adapted to the clusters of Pc s and networks of workstations available in most research laboratories.

As a first goal, we focused on parallelizing the graph construction algorithm, which is a bottleneck for verification, as it requires a considerable amount of memory to store all reachable states. For this purpose, we developed two tools [8] : Distributor splits the construction of a graph over N machines communicating using Tcp/Ip sockets; each machine builds a graph fragment, the distribution of states between the machines being determined by a static hash function; Bcg_Merge merges the N graph fragments constructed by Distributor to produce the entire graph.

Distributor  3.0 and Bcg_Merge  3.0 are now properly documented and integrated into Cadp . A tool paper was published at an international conference [27] .

In 2006, this work progressed as follows:

As a second goal, we aim at parallelizing on the fly verification itself. Because the Cæsar_Solve library (see §  6.1.1 ) is our central verification engine for both model checking, e.g., in the Evaluator tool (see §  6.1.3 ), and equivalence checking, e.g., in the Bisimulator (see §  6.1.2 ) and Reductor (see §  6.1.4 ) tools, we have been designing a distributed version of the Cæsar_Solve library to solve boolean equation systems on the fly using several machines.

In 2006, we continued the development of this library. The library code (16, 000 lines of C code) was thoroughly reviewed and simplified. The error management was improved. The primitive for writing a boolean equation system (or the portion of the system corresponding to the diagnostic of a given variable) to a file was also implemented in the distributed version of Cæsar_Solve . The distributed resolution algorithm for boolean equation systems was enhanced to detect on the fly cyclic dependencies between equation blocks (the presence of such dependencies indicates that the boolean equation system has an alternation depth greater than one).

An article about the distributed version of Cæsar_Solve and its applications was published in an international conference [28] .

We developed a new tool, named Bes_Solve , which supersedes two existing prototype tools for generating random boolean equation systems and for reading and writing boolean equation systems from/to text files, respectively. Bes_Solve allows to compare and cross-check the various resolution algorithms provided by the sequential and distributed versions of Cæsar_Solve . It constructs a boolean equation system in memory either by reading it from a (possibly compressed) text file, or by generating it randomly according to various parameters (number of equation blocks, minimum and maximum number of variables in each block, length of the equations, percentage of boolean constants, percentage of disjunctive and conjunctive variables in the right-hand sides of the equations, seed value for initializing the random number generator, etc.). Then, a boolean variable defined in some equation block of the boolean system can be solved by invoking any sequential or distributed algorithm of Cæsar_Solve . Bes_Solve served to experiment intensively the resolution algorithms and allowed to correct a bug in algorithm A4 of the sequential version of Cæsar_Solve .

Other Tool Developments

Participants : David Champelovier, Jérôme Fereyre, Hubert Garavel, Frédéric Lang, Nathalie Lépy, Radu Mateescu, Wendelin Serwe, Marie Vidal.

We undertook the design of an integrated development environment for Cadp within the Eclipse framework. This environment comprises both a Lotos editor and a graphical user-interface (inspired from Eucalyptus but based on Eclipse ) for the Cadp tools.

Additionally, we improved the following Cadp tools and libraries:

  • We fixed one bug in the Caesar_Regexp library and two bugs in Xtl .

  • We enhanced Determinator and Bcg_Min to support double precision floating point numbers.

  • We improved the Eucalyptus graphical user-interface to provide access to all recent features and tools of Cadp .

  • We added a new Cadp demo example (Web services for stock management and an on-line book auction) and we updated most of the other demo examples to take advantage of the most recent features and tools of Cadp .

We continued adapting Cadp to the latest computing platforms:

  • We finished porting Cadp to recent Linux distributions and Mac OS  10.4 ``Tiger ''.

  • We modified Cadp to support recent C compilers (Gcc  4, Intel Icc  9.0, Sun Studio  11).

  • We improved the portability of Cadp by adding new ``wrappers'', i.e., shell scripts that make Cadp less dependent on the underlying operating system.

  • As regards 64-bit architectures:

    • We wrote a portability guide for 64-bit applications.

    • We started porting the shell scripts of Cadp as well as third party software used by Cadp (e.g., Cudd , Sparse , Tcl-Tk/Tix , garbage collector) to 64-bit architectures.


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