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Formal Methods Forum
Autumn 2000
This is a seminar on formal methods in computer science and engineering
organized by the Laboratory for Theoretical Computer Science at HUT.
We meet usually on Fridays at 2 p.m. in room B353 in the Computer Science
building.
For further information, please contact
Ilkka Niemelä.
Program
- 1.9.2000 Petteri Kaski:
Enumeration of Balanced Ternary Designs
Abstract:
A (V, B; \rho_1, \rho_2, R; K, \Lambda) balanced ternary design
is a pair (X, Y), where X is a set of cardinality V, and Y
is a multiset of B multisets, or blocks, each consisting of K elements
of X. Each element of X must appear exactly R times in the
blocks of the design, \rho_1 times with multiplicity one, and \rho_2
times with multiplicity two. Additionally, every pair of distinct elements
of X must appear exactly \Lambda times in the blocks of the design.
Determining the number of nonisomorphic designs in a given class of
designs and explicitly constructing these designs are central problems
in design theory. The talk describes a backtrack search algorithm with
isomorph rejection that was used to carry out a constructive enumeration
for all but 12 of the 155 balanced ternary design classes in the range
V<=10, B<=30, R<=15.
(Joint work together with Patric Östergård).
- 15.9.2000 Timo Latvala:
Model Checking Linear Temporal Logic Properties of Petri Nets with
Fairness Constraints
Abstract: Verification of liveness properties of systems
requires in many cases fairness constraints to be imposed on the
system. In the context of modeling and analysis with Petri nets,
fairness constraints have been defined but the results have not been
extended to model checking. In this work Coloured Petri nets are
extended with fairness constraints on the transitions. The semantics of
the fairness constraints are defined with a fair Kripke structure. Model
checking linear temporal logic (LTL) properties of the Petri net is
facilitated by introducing a new LTL model checking procedure. The
procedure employs Streett automata to cope with the fairness constraints
efficiently. Also, new algorithms for the emptiness checking problem of
Streett automata and counterexample generation are presented. The new
procedure has been implemented in the MARIA analyzer. Some experiments
are performed to test the implementation and compare it with other ways
of coping with fairness constraints. The results show that the
procedure scales well when compared to alternative approaches.
- 6.10.2000 Marko Mäkelä:
Applying Compiler Techniques to Reachability Analysis of High-Level Models
Abstract:
Using a tool for high-level Petri nets as an example, we show how
techniques familiar from compilers can make reachability analysers
more powerful.
Syntax transformations can be applied to extend the modelling
language with convenient short-hand notations, such as universal and
existential quantification and multi-set summation.
The process of reachability analysis can be dramatically sped up by
compiling models to executable machine code that performs all
model-dependent tasks, such as computing the successors of a state.
This work describes some principal ideas behind code generation and
shows how generated code and static code can be linked together.
- 11.10.2000 Jussi Rintanen (Albert-Ludwigs-Universität Freiburg):
Automated Reasoning with Quantified Boolean Formulae
room TB357, at 3.00 p.m.
Abstract:
Quantified Boolean formulae (QBF) are an extension of the classical
propositional logic with universal and existential quantification
over truth-values. Interest in QBF stems from the fact that for
bounded-length prefixes they represent computational problems that
are complete for the levels of the polynomial hierarchy.
The representation of many computational problems between NP and PSPACE
is exponentially more concise in QBF than in the propositional logic.
In this talk I discuss techniques for automating reasoning with
quantified Boolean formulae. The main approach is to extend
the Davis-Putman-Logemann-Loveland with universal quantification.
We discuss this extension, additional inference rules made possible
by universal variables, problems arising from the more concise
representation, and preliminary solutions to these problems.
- 13.10.2000 Heikki Tauriainen:
Automated Testing of Büchi Automata Translators for Linear Temporal Logic
Abstract:
The formal verification of finite-state reactive and concurrent
systems against temporal logical requirements can be done by model
checking, which has the advantage of being well suited for automation.
However, reasoning about the correctness of systems using automated
techniques places high demands for ensuring the reliability of the model
checking tools themselves.
This work describes testing methods for detecting implementation errors in
a specific class of algorithms required in the automata-theoretic model
checking procedure for propositional linear temporal logic (LTL). These
algorithms are used for translating temporal requirements into Büchi
automata, which are used in the model checking process. Most of the test
methods can be easily integrated into an automatic testing tool for
translation algorithm implementations. Experimental results using a
randomized tool for testing the correctness of several implementations
included in real model checkers are presented. This testing has proved to
be an effective method for finding implementation errors in the
translators.
This work also presents a restricted LTL model checking algorithm designed
to work in a very simple subclass of systems, on which the analysis of
test failures is based. This algorithm can be used to automatically
confirm the incorrectness of a translation algorithm implementation.
- 27.10.2000 Silja Mäki:
Robust Membership Management for Ad-hoc Groups
Abstract:
In ad-hoc networks, the network nodes or users often form peer groups.
A group may share an application, a physical location, or
administrative tasks. Defining who is a member of the group is also
the first step towards establishing a shared secret key for secure
communication. Group membership management involves adding and
removing nodes in the group, as well as a method for authenticating
the group members. In this paper, we present a fully distributed,
certificate-based system for group membership management. It is
designed to suit highly dynamic ad-hoc networks where communications
is sporadic and nodes often fail unexpectedly.
- 24.11.2000 Harri Haanpää:
Sets in Z_n with Distinct Sums of Pairs
Abstract:
A subset S of an abelian group is a subset with distinct sums of pairs, if
for all i,j,m,n in S with i != j, m != n, and {i,j} != {m,n}, it holds that
i+j != m+n.
Let v_gamma(k) denote the least n such that there exists a k-element subset
of Z_n, the integers modulo n, with distinct sums of pairs (modulo n). An
orderly algorithm for computing values of v_gamma(k) is presented, values of
v_gamma for k <= 14 are given, and the connection to constant weight
error-correcting codes is discussed.
- 1.12.2000 Harriet Beaver and Teemu Tynjälä:
Modelling Feynman's Quantum Computer Using High-Level Petri Nets - A
Computational Approach
Abstract:
Petri Nets have been succesfully used to model systems based on classical
physics. The aim of our study is to model Feynman's quantum computer, one
of the first quantum computers suggested, using High-Level Petri
Nets. Feynman's quantum computer is based on a circuit of quantum logic
gates in a similar way as classical computers are based on boolean gates
and circuits. At the time of invention, Feynman could not give a time
bound for the completion of his computer's computation; a periodical
measuring procedure was needed. The periodical measurement allows us to
use a computational approach. We model the use and operation of Feynman's
computer using Predicate/Transition nets; the quantum mechanical
background of the operation is also described using the same
formalism. Naturally, in order to carry out the task of modelling
quantum mechanical phenomena, we had to extend Predicate/Transition net
formalism with complex numbers.
- 8.12.2000 Pierre-Olivier Ribet (LAAS, Toulouse):
Some LAAS Tools related to Petri Nets
Abstract:
This presentation gives an overview about two tools, TINA and Move.net,
which are related to Petri Nets and are currently under development at LAAS.
TINA is a sofware for the analysis of untimed and timed Petri Nets.
With respect to untimed systems, TINA allows the construction of
the Karp & Miller's covering tree and the check of the general
reachability properties (liveness, reversibility, absence of deadlock,
strong connected components, ....). The step approach has been also
implemented.
With respect to timed systems, TINA allows the construction of the
so-called
state class graph - that is a graph where timed states are symbolically
represented by a marking and a firing domain.
Move.net is an automatic graph displayer, which was written in Java, and
can display a mutable graph or Petri Net.
- 14.12.2000 Helger Lipmaa (Helsinki University of Technology,
Telecommunications Software and Multimedia Laboratory):
Efficient Algorithms for Differential Probability of Addition modulo 2^n
and Related Problems
Abstract:
Differential attacks against the block cipher work with
respect to XOR, or with respect to addition modulo $2^n$, for a fixed
$n>1$. In the case where a block cipher uses both XOR and addition
modulo $2^n$, it is important to know how these two operations relate to
each other. We present efficient algorithms for calculating the
differential properties of addition with respect to XOR. The first
algorithm computes, for a given differential
$\delta=(\DX,\DY\mapsto\DZ)$, the differential probability
$\DPA{n}(\delta):=
\mathbf{PR}_{x,y}[(x+y)\oplus((x\oplus\DX)+(y\oplus\DY))=\DZ]$ in the
worst-case time $\Theta(\log n)$ and in the average-case time
$\Theta(1)$. Next, we prove that the probability $\DPA{n}(\delta)\neq
0$, taken all differentials $\delta$, is $(1/2)\cdot (7/8)^{n-1}$, which
shows that addition has many easily found impossible differentials.
Additionally, we give formulas for other statistical properties of
$\DPA{n}$. Finally, we show how to find the maximal differential
probabilities of addition in the time $\Theta(\log n)$. The previously
known algorithms for computing the probabilities above are na{\"\i}ve,
requiring almost exhaustive computation.
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Latest update: 09 January 2005.
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