34 research outputs found
Reordering Rule Makes OBDD Proof Systems Stronger
Atserias, Kolaitis, and Vardi showed that the proof system of Ordered Binary Decision Diagrams with conjunction and weakening, OBDD(^, weakening), simulates CP^* (Cutting Planes with unary coefficients). We show that OBDD(^, weakening) can give exponentially shorter proofs than dag-like cutting planes. This is proved by showing that the Clique-Coloring tautologies have polynomial size proofs in the OBDD(^, weakening) system.
The reordering rule allows changing the variable order for OBDDs. We show that OBDD(^, weakening, reordering) is strictly stronger than OBDD(^, weakening). This is proved using the Clique-Coloring tautologies, and by transforming tautologies using coded permutations and orification. We also give CNF formulas which have polynomial size OBDD(^) proofs but require superpolynomial (actually, quasipolynomial size) resolution proofs, and thus we partially resolve an open question proposed by Groote and Zantema.
Applying dag-like and tree-like lifting techniques to the mentioned results, we completely analyze which of the systems among CP^*, OBDD(^), OBDD(^, reordering), OBDD(^, weakening) and OBDD(^, weakening, reordering) polynomially simulate each other. For dag-like proof systems, some of our separations are quasipolynomial and some are exponential; for tree-like systems, all of our separations are exponential
Proof Complexity of Systems of (Non-Deterministic) Decision Trees and Branching Programs
This paper studies propositional proof systems in which lines are sequents of decision trees or branching programs, deterministic or non-deterministic. Decision trees (DTs) are represented by a natural term syntax, inducing the system LDT, and non-determinism is modelled by including disjunction, ?, as primitive (system LNDT). Branching programs generalise DTs to dag-like structures and are duly handled by extension variables in our setting, as is common in proof complexity (systems eLDT and eLNDT).
Deterministic and non-deterministic branching programs are natural nonuniform analogues of log-space (L) and nondeterministic log-space (NL), respectively. Thus eLDT and eLNDT serve as natural systems of reasoning corresponding to L and NL, respectively.
The main results of the paper are simulation and non-simulation results for tree-like and dag-like proofs in LDT, LNDT, eLDT and eLNDT. We also compare them with Frege systems, constant-depth Frege systems and extended Frege systems
Separating Incremental and Non-Incremental Bottom-Up Compilation
The aim of a compiler is, given a function represented in some language, to generate an equivalent representation in a target language L. In bottom-up (BU) compilation of functions given as CNF formulas, constructing the new representation requires compiling several subformulas in L. The compiler starts by compiling the clauses in L and iteratively constructs representations for new subformulas using an "Apply" operator that performs conjunction in L, until all clauses are combined into one representation. In principle, BU compilation can generate representations for any subformulas and conjoin them in any way. But an attractive strategy from a practical point of view is to augment one main representation - which we call the core - by conjoining to it the clauses one at a time. We refer to this strategy as incremental BU compilation. We prove that, for known relevant languages L for BU compilation, there is a class of CNF formulas that admit BU compilations to L that generate only polynomial-size intermediate representations, while their incremental BU compilations all generate an exponential-size core
Model checking multi-agent systems
A multi-agent system (MAS) is usually understood as a system composed of interacting
autonomous agents. In this sense, MAS have been employed successfully as a modelling
paradigm in a number of scenarios, especially in Computer Science. However, the process
of modelling complex and heterogeneous systems is intrinsically prone to errors: for this
reason, computer scientists are typically concerned with the issue of verifying that a system
actually behaves as it is supposed to, especially when a system is complex.
Techniques have been developed to perform this task: testing is the most common technique,
but in many circumstances a formal proof of correctness is needed. Techniques
for formal verification include theorem proving and model checking. Model checking
techniques, in particular, have been successfully employed in the formal verification of
distributed systems, including hardware components, communication protocols, security
protocols.
In contrast to traditional distributed systems, formal verification techniques for MAS are
still in their infancy, due to the more complex nature of agents, their autonomy, and
the richer language used in the specification of properties. This thesis aims at making
a contribution in the formal verification of properties of MAS via model checking. In
particular, the following points are addressed:
• Theoretical results about model checking methodologies for MAS, obtained by
extending traditional methodologies based on Ordered Binary Decision Diagrams (OBDDS) for temporal logics to multi-modal logics for time, knowledge, correct behaviour, and strategies of agents. Complexity results for model checking these logics
(and their symbolic representations).
• Development of a software tool (MCMAS) that permits the specification and verification
of MAS described in the formalism of interpreted systems.
• Examples of application of MCMAS to various MAS scenarios (communication, anonymity, games, hardware diagnosability), including experimental results, and comparison with other tools available
Lightweight cryptography on ultra-constrained RFID devices
Devices of extremely small computational power like RFID tags are used in practice to a rapidly growing extent, a trend commonly referred to as ubiquitous computing. Despite their severely constrained resources, the security burden which these devices have to carry is often enormous, as their fields of application range from everyday access control to human-implantable chips providing sensitive medical information about a person. Unfortunately, established cryptographic primitives such as AES are way to 'heavy' (e.g., in terms of circuit size or power consumption) to be used in corresponding RFID systems, calling for new solutions and thus initiating the research area of lightweight cryptography.
In this thesis, we focus on the currently most restricted form of such devices and will refer to them as ultra-constrained RFIDs. To fill this notion with life and in order to create a profound basis for our subsequent cryptographic development, we start this work by providing a comprehensive summary of conditions that should be met by lightweight cryptographic schemes targeting ultra-constrained RFID devices.
Building on these insights, we then turn towards the two main topics of this thesis: lightweight authentication and lightweight stream ciphers. To this end, we first provide a general introduction to the broad field of authentication and study existing (allegedly) lightweight approaches.
Drawing on this, with the (n,k,L)^-protocol, we suggest our own lightweight authentication scheme and, on the basis of corresponding hardware implementations for FPGAs and ASICs, demonstrate its suitability for ultra-constrained RFIDs.
Subsequently, we leave the path of searching for dedicated authentication protocols and turn towards stream cipher design, where we first revisit some prominent classical examples and, in particular, analyze their state initialization algorithms.
Following this, we investigate the rather young area of small-state stream ciphers, which try to overcome the limit imposed by time-memory-data tradeoff (TMD-TO) attacks on the security of classical stream ciphers. Here, we present some new attacks, but also corresponding design ideas how to counter these.
Paving the way for our own small-state stream cipher, we then propose and analyze the LIZARD-construction, which combines the explicit use of packet mode with a new type of state initialization algorithm. For corresponding keystream generator-based designs of inner state length n, we prove a tight (2n/3)-bound on the security against TMD-TO key recovery attacks.
Building on these theoretical results, we finally present LIZARD, our new lightweight stream cipher for ultra-constrained RFIDs. Its hardware efficiency and security result from combining a Grain-like design with the LIZARD-construction. Most notably, besides lower area requirements, the estimated power consumption of LIZARD is also about 16 percent below that of Grain v1, making it particularly suitable for passive RFID tags, which obtain their energy exclusively through an electromagnetic field radiated by the reading device.
The thesis is concluded by an extensive 'Future Research Directions' chapter, introducing various new ideas and thus showing that the search for lightweight cryptographic solutions is far from being completed
Efficient local search for Pseudo Boolean Optimization
Algorithms and the Foundations of Software technolog
Abstraction in Model Checking Multi-Agent Systems
This thesis presents existential abstraction techniques for multi-agent systems preserving temporal-epistemic
specifications. Multi-agent systems, defined in the interpreted system frameworks,
are abstracted by collapsing the local states and actions of each agent. The goal of abstraction
is to reduce the state space of the system under investigation in order to cope with the state
explosion problem that impedes the verification of very large state space systems. Theoretical
results show that the resulting abstract system simulates the concrete one. Preservation
and correctness theorems are proved in this thesis. These theorems assure that if a temporal-epistemic
formula holds on the abstract system, then the formula also holds on the concrete
one. These results permit to verify temporal-epistemic formulas in abstract systems instead of
the concrete ones, therefore saving time and space in the verification process.
In order to test the applicability, usefulness, suitability, power and effectiveness of the abstraction
method presented, two different implementations are presented: a tool for data-abstraction
and one for variable-abstraction. The first technique achieves a state space reduction by collapsing
the values of the domains of the system variables. The second technique performs a
reduction on the size of the model by collapsing groups of two or more variables. Therefore, the
abstract system has a reduced number of variables. Each new variable in the abstract system
takes values belonging to a new domain built automatically by the tool. Both implementations
perform abstraction in a fully automatic way. They operate on multi agents models specified
in a formal language, called ISPL (Interpreted System Programming Language). This is the
input language for MCMAS, a model checker for multi-agent systems. The output is an ISPL
file as well (with a reduced state space).
This thesis also presents several suitable temporal-epistemic examples to evaluate both techniques.
The experiments show good results and point to the attractiveness of the temporal-epistemic
abstraction techniques developed in this thesis. In particular, the contributions of
the thesis are the following ones:
• We produced correctness and preservation theoretical results for existential abstraction.
• We introduced two algorithms to perform data-abstraction and variable-abstraction on
multi-agent systems.
• We developed two software toolkits for automatic abstraction on multi-agent scenarios:
one tool performing data-abstraction and the second performing variable-abstraction.
• We evaluated the methodologies introduced in this thesis by running experiments on
several multi-agent system examples
Selected Topics in Network Optimization: Aligning Binary Decision Diagrams for a Facility Location Problem and a Search Method for Dynamic Shortest Path Interdiction
This work deals with three different combinatorial optimization problems: minimizing the total size of a pair of binary decision diagrams (BDDs) under a certain structural property, a variant of the facility location problem, and a dynamic version of the Shortest-Path Interdiction (DSPI) problem. However, these problems all have the following core idea in common: They all stem from representing an optimization problem as a decision diagram. We begin from cases in which such a diagram representation of reasonable size might exist, but finding a small diagram is difficult to achieve. The first problem develops a heuristic for enforcing a structural property for a collection of BDDs, which allows them to be merged into a single one efficiently. In the second problem, we consider a specific combinatorial problem that allows for a natural representation by a pair of BDDs. We use the previous result and ideas developed earlier in the literature to reformulate this problem as a linear program over a single BDD. This approach enables us to obtain sensitivity information, while often enjoying runtimes comparable to a mixed integer program solved with a commercial solver, after we pay the computational overhead of building the diagram (e.g., when re-solving the problem using different costs, but the same graph topology). In the last part, we examine DSPI, for which building the full decision diagram is generally impractical. We formalize the concept of a game tree for the DSPI and design a heuristic based on the idea of building only selected parts of this exponentially-sized decision diagram (which is not binary any more). We use a Monte Carlo Tree Search framework to establish policies that are near optimal. To mitigate the size of the game tree, we leverage previously derived bounds for the DSPI and employ an alpha–beta pruning technique for minimax optimization. We highlight the practicality of these ideas in a series of numerical experiments