Transient Reward Approximation for Continuous-Time Markov Chains

We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power grids, of computer virus vulnerability, and in the study of crowd dynamics. We use abstraction techniques together with novel algorithms for the computation of bounds on the expected final and accumulated rewards in continuous-time Markov decision processes (CTMDPs). These ingredients are combined in a partly symbolic and partly explicit (symblicit) analysis approach. In particular, we circumvent the use of multi-terminal decision diagrams, because the latter do not work well if facing a large number of different rates. We demonstrate the practical applicability and efficiency of the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit

Verifying Computation Tree Logic of Knowledge via Knowledge-Oriented Petri Nets and Ordered Binary Decision Diagrams

Computation Tree Logic of Knowledge (CTLK) can specify many requirements of privacy and security of multi-agent systems (MAS). In our previous papers, we defined Knowledge-oriented Petri Net (KPN) to model MAS, proposed similar reachability graph to verify CTLK, gave their model checking algorithms and developed a related tool. In this paper, we use the technique of Ordered Binary Decision Diagrams (OBDD) to encode similar reachability graph in order to alleviate the state explosion problem, and verify more epistemic operators of CTLK. We design the corresponding symbolic model checking algorithms and improve our tool. We compare our model and method with MCMAS that is the state-of-the-art CTLK model checker, and experiments illustrate the advantages of our model and method. We also explain the reasons why our model and method can obtain better performances

On Model Based Synthesis of Embedded Control Software

Many Embedded Systems are indeed Software Based Control Systems (SBCSs), that is control systems whose controller consists of control software running on a microcontroller device. This motivates investigation on Formal Model Based Design approaches for control software. Given the formal model of a plant as a Discrete Time Linear Hybrid System and the implementation specifications (that is, number of bits in the Analog-to-Digital (AD) conversion) correct-by-construction control software can be automatically generated from System Level Formal Specifications of the closed loop system (that is, safety and liveness requirements), by computing a suitable finite abstraction of the plant. With respect to given implementation specifications, the automatically generated code implements a time optimal control strategy (in terms of set-up time), has a Worst Case Execution Time linear in the number of AD bits $b$, but unfortunately, its size grows exponentially with respect to $b$. In many embedded systems, there are severe restrictions on the computational resources (such as memory or computational power) available to microcontroller devices. This paper addresses model based synthesis of control software by trading system level non-functional requirements (such us optimal set-up time, ripple) with software non-functional requirements (its footprint). Our experimental results show the effectiveness of our approach: for the inverted pendulum benchmark, by using a quantization schema with 12 bits, the size of the small controller is less than 6% of the size of the time optimal one.Comment: Accepted for publication by EMSOFT 2012. arXiv admin note: substantial text overlap with arXiv:1107.5638,arXiv:1207.409

Multi-Domain Surety Modeling and Analysis for High Assurance Systems

Engineering systems are becoming increasingly complex as state of the art technologies am incorporated into designs. Surety modeling and analysis is an emerging science that permits an engineer to qualitatively and quantitatively predict and assess the completeness and predictability of a design. Surety is a term often used in the Department of Defense (DoD) and Department of Energy (DOE) communities, which refers to the integration of safety, security, reliability and performance aspects of design. Current risk assessment technologies for analyzing complex systems fail to adequately describe the problem, thus making assessment fragmented and non-integrated. To address this problem, we have developed a methodology and extensible software tool set to address model integration and complexity for high consequence systems. The MultiGraph Architecture (MGA) facilitates multi-domain, model-integrated modeling and analyses of complex, high-assurance systems. The MGA modeling environment allows the engineer to customize the modeling environment to match a design paradigm representative of the actual design. Previous modeling tools have a point-defined model space that forms the modeler to work in less than optimal environments. Current approaches for the problem to be bounded and constrained by requirements of the modeling tool and not the actual design problem. In some small cases, this is only maximally adequate MM facilitates the implementation of a surety methodology, which is used to represent high assurance systems with respect to safety and reliability. Formal mathematical models am used to correctly describe design safety and reliability functionality and behavioral fictional and behavioral representations of the design w then analyzed using commercial-off-the-shelf tools

Processing Succinct Matrices and Vectors

We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of a semiring (instead of 0 and 1). A simple example shows that the product of two MTDD-represented matrices cannot be represented by an MTDD of polynomial size. To overcome this deficiency, we extended MTDDs to MTDD_+ by allowing componentwise symbolic addition of variables (of the same dimension) in rules. It is shown that accessing an entry, equality checking, matrix multiplication, and other basic matrix operations can be solved in polynomial time for MTDD_+-represented matrices. On the other hand, testing whether the determinant of a MTDD-represented matrix vanishes PSPACE$-complete, and the same problem is NP-complete for MTDD_+-represented diagonal matrices. Computing a specific entry in a product of MTDD-represented matrices is #P-complete.Comment: An extended abstract of this paper will appear in the Proceedings of CSR 201

The Language of Search

This paper is concerned with a class of algorithms that perform exhaustive search on propositional knowledge bases. We show that each of these algorithms defines and generates a propositional language. Specifically, we show that the trace of a search can be interpreted as a combinational circuit, and a search algorithm then defines a propositional language consisting of circuits that are generated across all possible executions of the algorithm. In particular, we show that several versions of exhaustive DPLL search correspond to such well-known languages as FBDD, OBDD, and a precisely-defined subset of d-DNNF. By thus mapping search algorithms to propositional languages, we provide a uniform and practical framework in which successful search techniques can be harnessed for compilation of knowledge into various languages of interest, and a new methodology whereby the power and limitations of search algorithms can be understood by looking up the tractability and succinctness of the corresponding propositional languages