@phdthesis{4559,
abstract = {We study games played on graphs with omega-regular conditions specified as parity, Rabin, Streett or Muller conditions. These games have applications in the verification, synthesis, modeling, testing, and compatibility checking of reactive systems. Important distinctions between graph games are as follows: (a) turn-based vs. concurrent games, depending on whether at a state of the game only a single player makes a move, or players make moves simultaneously; (b) deterministic vs. stochastic, depending on whether the transition function is a deterministic or a probabilistic function over successor states; and (c) zero-sum vs. non-zero-sum, depending on whether the objectives of the players are strictly conflicting or not.
We establish that the decision problem for turn-based stochastic zero-sum games with Rabin, Streett, and Muller objectives are NP-complete, coNP-complete, and PSPACE-complete, respectively, substantially improving the previously known 3EXPTIME bound. We also present strategy improvement style algorithms for turn-based stochastic Rabin and Streett games. In the case of concurrent stochastic zero-sum games with parity objectives we obtain a PSPACE bound, again improving the previously known 3EXPTIME bound. As a consequence, concurrent stochastic zero-sum games with Rabin, Streett, and Muller objectives can be solved in EXPSPACE, improving the previously known 4EXPTIME bound. We also present an elementary and combinatorial proof of the existence of memoryless \epsilon-optimal strategies in concurrent stochastic games with reachability objectives, for all real \epsilon>0, where an \epsilon-optimal strategy achieves the value of the game with in \epsilon against all strategies of the opponent. We also use the proof techniques to present a strategy improvement style algorithm for concurrent stochastic reachability games.
We then go beyond \omega-regular objectives and study the complexity of an important class of quantitative objectives, namely, limit-average objectives. In the case of limit-average games, the states of the graph is labeled with rewards and the goal is to maximize the long-run average of the rewards. We show that concurrent stochastic zero-sum games with limit-average objectives can be solved in EXPTIME.
Finally, we introduce a new notion of equilibrium, called secure equilibrium, in non-zero-sum games which captures the notion of conditional competitiveness. We prove the existence of unique maximal secure equilibrium payoff profiles in turn-based deterministic games, and present algorithms to compute such payoff profiles. We also show how the notion of secure equilibrium extends the assume-guarantee style of reasoning in the game theoretic framework.},
author = {Krishnendu Chatterjee},
pages = {1 -- 247},
publisher = {University of California, Berkeley},
title = {{Stochastic ω-Regular Games}},
year = {2007},
}
@phdthesis{4566,
abstract = {Complex system design today calls for compositional design and implementation. However each component is designed with certain assumptions about the environment it is meant to operate in, and delivering certain guarantees if those assumptions are satisfied; numerous inter-component interaction errors are introduced in the manual and error-prone integration process as there is little support in design environments for machine-readably representing these assumptions and guarantees and automatically checking consistency during integration.
Based on Interface Automata we propose a framework for compositional design and analysis of systems: a set of domain-specific automata-theoretic type systems for compositional system specification and analysis by behavioral specification of open systems. We focus on three different domains: component-based hardware systems communicating on bidirectional wires. concurrent distributed recursive message-passing software systems, and embedded software system components operating in resource-constrained environments. For these domains we present approaches to formally represent the assumptions and conditional guarantees between interacting open system components. Composition of such components produces new components with the appropriate assumptions and guarantees. We check satisfaction of temporal logic specifications by such components, and the substitutability of one component with another in an arbitrary context. Using this framework one can analyze large systems incrementally without needing extensive summary information to close the system at each stage. Furthermore, we focus only on the inter-component interaction behavior without dealing with the full implementation details of each component. Many of the merits of automata-theoretic model-checking are combined with the compositionality afforded by type-system based techniques. We also present an integer-based extension of the conventional boolean verification framework motivated by our interface formalism for embedded software components.
Our algorithms for checking the behavioral compatibility of component interfaces are available in our tool Chic, which can be used as a plug-in for the Java IDE JBuilder and the heterogenous modeling and design environment Ptolemy II.
Finally, we address the complementary problem of partitioning a large system into meaningful coherent components by analyzing the interaction patterns between its basic elements. We demonstrate the usefulness of our partitioning approach by evaluating its efficacy in improving unit-test branch coverage for a large software system implemented in C.},
author = {Chakrabarti, Arindam},
pages = {1 -- 244},
publisher = {University of California, Berkeley},
title = {{A framework for compositional design and analysis of systems}},
year = {2007},
}
@phdthesis{4236,
author = {de Vladar, Harold},
publisher = {Centro de estudios avazados, IVIC},
title = {{Métodos no lineales y sus aplicaciones en dinámicas aleatorias de poblaciones celulares}},
doi = {3810},
year = {2004},
}
@phdthesis{4424,
abstract = {The enormous cost and ubiquity of software errors necessitates the need for techniques and tools that can precisely analyze large systems and prove that they meet given specifications, or if they don't, return counterexample behaviors showing how the system fails. Recent advances in model checking, decision procedures, program analysis and type systems, and a shift of focus to partial specifications common to several systems (e.g., memory safety and race freedom) have resulted in several practical verification methods. However, these methods are either precise or they are scalable, depending on whether they track the values of variables or only a fixed small set of dataflow facts (e.g., types), and are usually insufficient for precisely verifying large programs.
We describe a new technique called Lazy Abstraction (LA) which achieves both precision and scalability by localizing the use of precise information. LA automatically builds, explores and refines a single abstract model of the program in a way that different parts of the model exhibit different degrees of precision, namely just enough to verify the desired property. The algorithm automatically mines the information required by partitioning mechanical proofs of unsatisfiability of spurious counterexamples into Craig Interpolants. For multithreaded systems, we give a new technique based on analyzing the behavior of a single thread executing in a context which is an abstraction of the other (arbitrarily many) threads. We define novel context models and show how to automatically infer them and analyze the full system (thread + context) using LA.
LA is implemented in BLAST. We have run BLAST on Windows and Linux Device Drivers to verify API conformance properties, and have used it to find (or guarantee the absence of) data races in multithreaded Networked Embedded Systems (NESC) applications. BLAST is able to prove the absence of races in several cases where earlier methods, which depend on lock-based synchronization, fail.},
author = {Jhala, Ranjit},
pages = {1 -- 165},
publisher = {University of California, Berkeley},
title = {{Program verification by lazy abstraction}},
year = {2004},
}
@phdthesis{2414,
author = {Uli Wagner},
publisher = {ETH Zurich},
title = {{On k-Sets and Their Applications}},
doi = {10.3929/ethz-a-004708408},
year = {2003},
}
@phdthesis{3678,
author = {Christoph Lampert},
booktitle = {Bonner Mathematische Schriften},
pages = {1 -- 165},
publisher = {Universität Bonn, Fachbibliothek Mathematik},
title = {{The Neumann operator in strictly pseudoconvex domains with weighted Bergman metric }},
volume = {356},
year = {2003},
}
@phdthesis{4416,
abstract = {Methods for the formal specification and verification of systems are indispensible for the development of complex yet correct systems. In formal verification, the designer describes the system in a modeling language with a well-defined semantics, and this system description is analyzed against a set of correctness requirements. Model checking is an algorithmic technique to check that a system description indeed satisfies correctness requirements given as logical specifications. While successful in hardware verification, the potential for model checking for software and embedded systems has not yet been realized. This is because traditional model checking focuses on systems modeled as finite state-transition graphs. While a natural model for hardware (especially synchronous hardware), state-transition graphs often do not capture software and embedded systems at an appropriate level of granularity. This dissertation considers two orthogonal extensions to finite state-transition graphs making model checking techniques applicable to both a wider class of systems and a wider class of properties.
The first direction is an extension to infinite-state structures finitely represented using constraints and operations on constraints. Infinite state arises when we wish to model variables with unbounded range (e.g., integers), or data structures, or real time. We provide a uniform framework of symbolic region algebras to study model checking of infinite-state systems. We also provide sufficient language-independent termination conditions for symbolic model checking algorithms on infinite state systems.
The second direction supplements verification with game theoretic reasoning. Games are natural models for interactions between components. We study game theoretic behavior with winning conditions given by temporal logic objectives both in the deterministic and in the probabilistic context. For deterministic games, we provide an extremal model characterization of fixpoint algorithms that link solutions of verification problems to solutions for games. For probabilistic games we study fixpoint characterization of winning probabilities for games with omega-regular winning objectives, and construct (epsilon-)optimal winning strategies.},
author = {Majumdar, Ritankar},
pages = {1 -- 201},
publisher = {University of California, Berkeley},
title = {{Symbolic algorithms for verification and control}},
year = {2003},
}
@phdthesis{4425,
abstract = {Giotto provides a time-triggered programmer’s model for the implementation of embedded control systems with hard real-time constraints. Giotto’s precise semantics and predictabil- ity make it suitable for safety-critical applications.
Giotto is based around the idea that time-triggered task invocation together with time-triggered mode switching can form a useful programming model for real-time systems. To substantiate this claim, we describe the use of Giotto to refactor the software of a small, autonomous helicopter. The ease with which Giotto expresses the existing software provides evidence that Giotto is an appropriate programming language for control systems.
Since Giotto is a real-time programming language, ensuring that Giotto programs meet their deadlines is crucial. To study precedence-constrained Giotto scheduling, we first examine single-mode, single-processor scheduling. We extend to an infinite, periodic setting the classical problem of meeting deadlines for a set of tasks with release times, deadlines, precedence constraints, and preemption. We then develop an algorithm for scheduling Giotto programs on a single processor by representing Giotto programs as instances of the extended scheduling problem.
Next, we study multi-mode, single-processor Giotto scheduling. This problem is different from classical scheduling problems, since in our precedence-constrained approach, the deadlines of tasks may vary depending on the mode switching behavior of the program. We present conditional scheduling models which capture this varying-deadline behavior. We develop polynomial-time algorithms for some conditional scheduling models, and prove oth- ers to be computationally hard. We show how to represent multi-mode Giotto programs as instances of the model, resulting in an algorithm for scheduling multi-mode Giotto programs on a single processor.
Finally, we show that the problem of scheduling Giotto programs for multiple net- worked processors is strongly NP-hard.},
author = {Horowitz, Benjamin},
pages = {1 -- 237},
publisher = {University of California, Berkeley},
title = {{Giotto: A time-triggered language for embedded programming}},
year = {2003},
}
@phdthesis{4414,
abstract = {This dissertation investigates game-theoretic approaches to the algorithmic analysis of concurrent, reactive systems. A concurrent system comprises a number of components working concurrently; a reactive system maintains an ongoing interaction with its environment. Traditional approaches to the formal analysis of concurrent reactive systems usually view the system as an unstructured state-transition graphs; instead, we view them as collections of interacting components, where each one is an open system which accepts inputs from the other components. The interactions among the components are naturally modeled as games.
Adopting this game-theoretic view, we study three related problems pertaining to the verification and synthesis of systems. Firstly, we propose two novel game-theoretic techniques for the model-checking of concurrent reactive systems, and improve the performance of model-checking. The first technique discovers an error as soon as it cannot be prevented, which can be long before it actually occurs. This technique is based on the key observation that "unpreventability" is a local property to a module: an error is unpreventable in a module state if no environment can prevent it. The second technique attempts to decompose a model-checking proof into smaller proof obligations by constructing abstract modules automatically, using reachability and "unpreventability" information about the concrete modules. Three increasingly powerful proof decomposition rules are proposed and we show that in practice, the resulting abstract modules are often significantly smaller than the concrete modules and can drastically reduce the space and time requirements for verification. Both techniques fall into the category of compositional reasoning.
Secondly, we investigate the composition and control of synchronous systems. An essential property of synchronous systems for compositional reasoning is non-blocking. In the composition of synchronous systems, however, due to circular causal dependency of input and output signals, non-blocking is not always guaranteed. Blocking compositions of systems can be ruled out semantically, by insisting on the existence of certain fixed points, or syntactically, by equipping systems with types, which make the dependencies between input and output signals transparent. We characterize various typing mechanisms in game-theoretic terms, and study their effects on the controller synthesis problem. We show that our typing systems are general enough to capture interesting real-life synchronous systems such as all delay-insensitive digital circuits. We then study their corresponding single-step control problems --a restricted form of controller synthesis problem whose solutions can be iterated in appropriate manners to solve all LTL controller synthesis problems. We also consider versions of the controller synthesis problem in which the type of the controller is given. We show that the solution of these fixed-type control problems requires the evaluation of partially ordered (Henkin) quantifiers on boolean formulas, and is therefore harder (nondeterministic exponential time) than more traditional control questions.
Thirdly, we study the synthesis of a class of open systems, namely, uninitialized state machines. The sequential synthesis problem, which is closely related to Church's solvability problem, asks, given a specification in the form of a binary relation between input and output streams, for the construction of a finite-state stream transducer that converts inputs to appropriate outputs. For efficiency reasons, practical sequential hardware is often designed to operate without prior initialization. Such hardware designs can be modeled by uninitialized state machines, which are required to satisfy their specification if started from any state. We solve the sequential synthesis problem for uninitialized systems, that is, we construct uninitialized finite-state stream transducers. We consider specifications given by LTL formulas, deterministic, nondeterministic, universal, and alternating Buechi automata. We solve this uninitialized synthesis problem by reducing it to the well-understood initialized synthesis problem. While our solution is straightforward, it leads, for some specification formalisms, to upper bounds that are exponentially worse than the complexity of the corresponding initialized problems. However, we prove lower bounds to show that our simple solutions are optimal for all considered specification formalisms. The lower bound proofs require nontrivial generic reductions.},
author = {Mang, Freddy},
pages = {1 -- 116},
publisher = {University of California, Berkeley},
title = {{Games in open systems verification and synthesis}},
year = {2002},
}
@phdthesis{4411,
abstract = {Model checking algorithms for the verification of reactive systems proceed by a systematic and exhaustive exploration of the system state space. They do not scale to large designs because of the state explosion problem --the number of states grows exponentially with the number of components in the design. Consequently, the model checking problem is PSPACE-hard in the size of the design description. This dissertation proposes three novel techniques to combat the state explosion problem.
One of the most important advances in model checking in recent years has been the discovery of symbolic methods, which use a calculus of expressions, such as binary decision diagrams, to represent the state sets encountered during state space exploration. Symbolic model checking has proved to be effective for verifying hardware designs. Traditionally, symbolic checking of temporal logic specifications is performed by backward fixpoint reasoning with the operator Pre. Backward reasoning can be wasteful since unreachable states are explored. We suggest the use of forward fixpoint reasoning based on the operator Post. We show how all linear temporal logic specifications can be model checked symbolically by forward reasoning. In contrast to backward reasoning, forward reasoning performs computations only on the reachable states.
Heuristics that improve algorithms for application domains, such as symbolic methods for hardware designs, are useful but not enough to make model checking feasible on industrial designs. Currently, exhaustive state exploration is possible only on designs with about 50-100 boolean state variables. Assume-guarantee verification attempts to combat the state explosion problem by using the principle of "divide and conquer," where the components of the implementation are analyzed one at a time. Typically, an implementation component refines its specification only when its inputs are suitably constrained by other components in the implementation. The assume-guarantee principle states that instead of constraining the inputs by implementation components, it is sound to constrain them by the corresponding specification components, which can be significantly smaller. We extend the assume-guarantee proof rule to deal with the case where the specification operates at a coarser time scale than the implementation. Using our model checker Mocha, which implements this methodology, we verify VGI, a parallel DSP processor chip with 64 compute processors each containing approximately 800 state variables and 30K gates.
Our third contribution is a systematic model checking methodology for verifying the abstract shared-memory interface of sequential consistency on multiprocessor systems with three parameters --number of processors, number of memory locations, and number of data values. Sequential consistency requires that some interleaving of the local temporal orders of read/write events at different processors be a trace of serial memory. Therefore, it suffices to construct a non-interfering serializer that watches and reorders read/write events so that a trace of serial memory is obtained. While in general such a serializer must be unbounded even for fixed values of the parameters --checking sequential consistency is undecidable!-- we show that the paradigmatic class of snoopy cache coherence protocols has finite-state serializers. In order to reduce the arbitrary-parameter problem to the fixed-parameter problem, we develop a novel framework for induction over the number of processors and use the notion of a serializer to reduce the problem of verifying sequential consistency to that of checking language inclusion between finite state machines.},
author = {Qadeer, Shaz},
pages = {1 -- 150},
publisher = {University of California, Berkeley},
title = {{Algorithms and Methodology for Scalable Model Checking}},
year = {1999},
}
@phdthesis{4419,
author = {Kopke, Peter},
publisher = {Cornell University},
title = {{The Theory of Rectangular Hybrid Automata}},
year = {1996},
}
@phdthesis{4428,
abstract = {Hybrid systems are real-time systems that react to both discrete and continuous activities (such as analog signals, time, temperature, and speed). Typical examples of hybrid systems are embedded systems, timing-based communication protocols, and digital circuits at the transistor level. Due to the rapid development of microprocessor technology, hybrid systems directly control much of what we depend on in our daily lives. Consequently, the formal specification and verification of hybrid systems has become an active area of research. This dissertation presents the first general framework for the formal specification and verification of hybrid systems, as well as the first hybrid-system analysis tool--HyTech. The framework consists of a graphical finite-state-machine-like language for modeling hybrid systems, a temporal logic for modeling the requirements of hybrid systems, and a computer procedure that verifies modeled hybrid systems against modeled requirements. The tool HyTech is the implementation of the framework using C++ and Mathematica.
More specifically, our hybrid-system modeling language, Hybrid Automata, is an extension of timed automata with discrete and continuous variables whose dynamics are governed by differential equations. Our requirement modeling language, ICTL, is a branching-time temporal logic, and is an extension of TCTL with stop-watch variables. Our verification procedure is a symbolic model-checking procedure that verifies linear hybrid automata against ICTL formulas. To make HyTech more efficient and effective, we use model-checking strategies and abstract operators that can expedite the verification process. To enable HyTech to verify nonlinear hybrid automata, we introduce two translations from nonlinear hybrid automata to linear hybrid automata. We have applied HyTech to analyze more than 30 hybrid-system benchmarks. In this dissertation, we present the application of HyTech to three nontrivial hybrid systems taken from the literature.},
author = {Ho, Pei},
pages = {1 -- 188},
publisher = {Cornell University},
title = {{Automatic Analysis of Hybrid Systems}},
doi = {CSD-TR95-1536},
year = {1995},
}
@phdthesis{4516,
author = {Thomas Henzinger},
publisher = {Stanford University},
title = {{The Temporal Specification and Verification of Real-time Systems }},
year = {1991},
}
@phdthesis{4337,
author = {Nicholas Barton},
publisher = {University of East Anglia},
title = {{A hybrid zone in the alpine grasshopper Podisma pedestris}},
year = {1979},
}