A uniform framework for modelling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences

Labeled transition systems are typically used as behavioral models of concurrent processes, and the labeled transitions define the a one-step state-to-state reachability relation. This model can be made generalized by modifying the transition relation to associate a state reachability distribution, rather than a single target state, with any pair of source state and transition label. The state reachability distribution becomes a function mapping each possible target state to a value that expresses the degree of one-step reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture well-known models of fully nondeterministic processes (LTS), fully probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and of nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. These can be defined on ULTraS by relying on appropriate measure functions that expresses the degree of reachability of a set of states when performing single-step or multi-step computations. It is shown that the specializations of bisimulation, trace, and testing equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models

A Deductive Approach towards Reasoning about Algebraic Transition Systems

Algebraic transition systems are extended from labeled transition systems by allowing transitions labeled by algebraic equations for modeling more complex systems in detail. We present a deductive approach for specifying and verifying algebraic transition systems. We modify the standard dynamic logic by introducing algebraic equations into modalities. Algebraic transition systems are embedded in modalities of logic formulas which specify properties of algebraic transition systems. The semantics of modalities and formulas is defined with solutions of algebraic equations. A proof system for this logic is constructed to verify properties of algebraic transition systems. The proof system combines with inference rules decision procedures on the theory of polynomial ideals to reduce a proof-search problem to an algebraic computation problem. The proof system proves to be sound but inherently incomplete. Finally, a typical example illustrates that reasoning about algebraic transition systems with our approach is feasible

Data-parallel concurrent constraint programming.

by Bo-ming Tong.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 104-[110]).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Concurrent Constraint Programming --- p.2Chapter 1.2 --- Finite Domain Constraints --- p.3Chapter 2 --- The Firebird Language --- p.5Chapter 2.1 --- Finite Domain Constraints --- p.6Chapter 2.2 --- The Firebird Computation Model --- p.6Chapter 2.3 --- Miscellaneous Features --- p.7Chapter 2.4 --- Clause-Based N on determinism --- p.9Chapter 2.5 --- Programming Examples --- p.10Chapter 2.5.1 --- Magic Series --- p.10Chapter 2.5.2 --- Weak Queens --- p.14Chapter 3 --- Operational Semantics --- p.15Chapter 3.1 --- The Firebird Computation Model --- p.16Chapter 3.2 --- The Firebird Commit Law --- p.17Chapter 3.3 --- Derivation --- p.17Chapter 3.4 --- Correctness of Firebird Computation Model --- p.18Chapter 4 --- Exploitation of Data-Parallelism in Firebird --- p.24Chapter 4.1 --- An Illustrative Example --- p.25Chapter 4.2 --- Mapping Partitions to Processor Elements --- p.26Chapter 4.3 --- Masks --- p.27Chapter 4.4 --- Control Strategy --- p.27Chapter 4.4.1 --- A Control Strategy Suitable for Linear Equations --- p.28Chapter 5 --- Data-Parallel Abstract Machine --- p.30Chapter 5.1 --- Basic DPAM --- p.31Chapter 5.1.1 --- Hardware Requirements --- p.31Chapter 5.1.2 --- Procedure Calling Convention And Process Creation --- p.32Chapter 5.1.3 --- Memory Model --- p.34Chapter 5.1.4 --- Registers --- p.41Chapter 5.1.5 --- Process Management --- p.41Chapter 5.1.6 --- Unification --- p.49Chapter 5.1.7 --- Variable Table --- p.49Chapter 5.2 --- DPAM with Backtracking --- p.50Chapter 5.2.1 --- Choice Point --- p.52Chapter 5.2.2 --- Trailing --- p.52Chapter 5.2.3 --- Recovering the Process Queues --- p.57Chapter 6 --- Implementation --- p.58Chapter 6.1 --- The DECmpp Massively Parallel Computer --- p.58Chapter 6.2 --- Implementation Overview --- p.59Chapter 6.3 --- Constraints --- p.60Chapter 6.3.1 --- Breaking Down Equality Constraints --- p.61Chapter 6.3.2 --- Processing the Constraint 'As Is' --- p.62Chapter 6.4 --- The Wide-Tag Architecture --- p.63Chapter 6.5 --- Register Window --- p.64Chapter 6.6 --- Dereferencing --- p.65Chapter 6.7 --- Output --- p.66Chapter 6.7.1 --- Collecting the Solutions --- p.66Chapter 6.7.2 --- Decoding the solution --- p.68Chapter 7 --- Performance --- p.69Chapter 7.1 --- Uniprocessor Performance --- p.71Chapter 7.2 --- Solitary Mode --- p.73Chapter 7.3 --- Bit Vectors of Domain Variables --- p.75Chapter 7.4 --- Heap Consumption of the Heap Frame Scheme --- p.77Chapter 7.5 --- Eager Nondeterministic Derivation vs Lazy Nondeterministic Deriva- tion --- p.78Chapter 7.6 --- Priority Scheduling --- p.79Chapter 7.7 --- Execution Profile --- p.80Chapter 7.8 --- Effect of the Number of Processor Elements on Performance --- p.82Chapter 7.9 --- Change of the Degree of Parallelism During Execution --- p.84Chapter 8 --- Related Work --- p.88Chapter 8.1 --- Vectorization of Prolog --- p.89Chapter 8.2 --- Parallel Clause Matching --- p.90Chapter 8.3 --- Parallel Interpreter --- p.90Chapter 8.4 --- Bounded Quantifications --- p.91Chapter 8.5 --- SIMD MultiLog --- p.91Chapter 9 --- Conclusion --- p.93Chapter 9.1 --- Limitations --- p.94Chapter 9.1.1 --- Data-Parallel Firebird is Specialized --- p.94Chapter 9.1.2 --- Limitations of the Implementation Scheme --- p.95Chapter 9.2 --- Future Work --- p.95Chapter 9.2.1 --- Extending Firebird --- p.95Chapter 9.2.2 --- Improvements Specific to DECmpp --- p.99Chapter 9.2.3 --- Labeling --- p.100Chapter 9.2.4 --- Parallel Domain Consistency --- p.101Chapter 9.2.5 --- Branch and Bound Algorithm --- p.102Chapter 9.2.6 --- Other Possible Future Work --- p.102Bibliography --- p.10

ROUTING TOPOLOGY RECOVERY FOR WIRELESS SENSOR NETWORKS

Liu, Rui Ph.D., Purdue University, December 2014. Routing Topology Recovery for Wireless Sensor Networks. Major Professor: Yao Liang

Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201

Formal Methods for Autonomous Systems

Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications, which are analogous to behaviors and requirements in system design and give us the means to verify and synthesize system behaviors with formal guarantees. This monograph provides a survey of the current state of the art on applications of formal methods in the autonomous systems domain. We consider correct-by-construction synthesis under various formulations, including closed systems, reactive, and probabilistic settings. Beyond synthesizing systems in known environments, we address the concept of uncertainty and bound the behavior of systems that employ learning using formal methods. Further, we examine the synthesis of systems with monitoring, a mitigation technique for ensuring that once a system deviates from expected behavior, it knows a way of returning to normalcy. We also show how to overcome some limitations of formal methods themselves with learning. We conclude with future directions for formal methods in reinforcement learning, uncertainty, privacy, explainability of formal methods, and regulation and certification

Dagstuhl News January - December 2001

"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic