) Leo Bachmair and Ashish Tiwari Department of Computer Science, SUNY at Stony Brook, Stony Brook, NY 11794, U.S.A fleo,astiwarig@cs.sunysb.edu 1 Introduction Kanellakis and Revesz [3] clarified the directional duality between congruence closure and unification closure by showing suitable

yet. We will break it down into solved cases and then pose an interesting open Interest has been growing in the termination of linear programs problem. This problem tries to see if there is an input for which the program does not terminate (or terminates only under certain conditions). Ashish Tiwari’s

Dr. Ashish Roy

special thanks to Dr. Ashish Tiwari who has been a most helpful collaborator over the last couple of years. Without his very precious time and help on this research, this dissertation might have taken much more time and possible a very different form. He has been very approachable and

Abstract. We show that termination is decidable for rewrite systems that contain shallow and right-linear rules, collapsing rules, and rightground rules. This class of rewrite systems is expressive enough to include interesting rules. Our proof uses the fact that this class of rewrite systems is known to be regularity-preserving and hence the reachability and joinability problems are decidable. Decidability of termination is obtained by analyzing the nonterminating derivations. 1 Introduction Term rewriting systems are Turing-complete models of computation that specifyrules for replacing certain patterns in terms by equivalent, in some cases simpler, other terms. Simpler models of computation result by imposing additionalconstraints on the form of terms in a rewrite system. For instance, if variables are not allowed, we get ground term rewrite system, which have been extensivelystudied, mainly via mapping them to tree automata [2]. More complex models of computation arise by allowing restricted variable occurrences in the term rewritesystem (or the tree automata transitions).

I examine the information content of a limit order book in a purely order-driven market. I analyze how the state of the limit order book affects a trader’s strategy. I develop an econometric technique to study order aggressiveness and provide empirical evidence on the recent theoretical models on limit order book markets. My results show that patient traders become more aggressive when the own (opposite) side book is thicker (thinner), the spread wider, and the temporary volatility increases. Also, I find that the buy and the sell sides of the book affect the order submission differently.

We present a technique based on the use of the quantier elimination decision procedure for real closed elds and simple theorem proving to construct a series of successively ner qualitative abstractions of hybrid automata. The resulting abstractions are always discrete transition systems which can then be used by any traditional analysis tool. The constructed abstractions are conservative and can be used to establish safety properties of the original system. Our technique works on linear and non-linear polynomial hybrid systems, that is, the guards on discrete transitions and the continuous ows in all modes can be specied using arbitrary polynomial expressions over the continuous variables. We have a prototype tool in the SAL environment which is built over the theorem prover PVS. The technique promises to scale well to large and complex hybrid systems. 1 1

This e-book is devoted to Global Optimization algorithms, which are methods for finding solutions of high quality for an incredible wide range of problems. We introduce the basic concepts of optimization and discuss features which make optimization problems difficult and thus, should be considered when trying to solve them. In this book, we focus on

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Today, abstract interpretation is capable of inferring a wide variety of quantifier-free program invariants. In this paper, we describe a general technique for building powerful quantified abstract domains that leverage existing quantifier-free domains. For example, from a domain that abstracts facts like a[1] = 0, we automatically construct a domain that can represent universally quantified facts like ∀i(0 ≤ i < n ⇒ a[i] = 0). The principal challenge in building such a domain is that, while most domains supply over-approximations of operations like join, meet, and variable elimination, working with the guards of quantified facts requires under-approximation. A crucial component of our approach is an automatic technique to convert the standard over-approximation operations provided with all domains into sound under-approximations. The correctness of our abstract interpreters is established by identifying two lattices–one that establishes the soundness of the abstract interpreter and another that defines its precision, or completeness. Despite the computational intractability of inferring quantified facts in general, we prove that the analyses we generate are complete relative to a very natural partial order. interpreters on top of domains for linear arithmetic, uninterpreted function symbols (used to model heap accesses), and pointer reachability. Our experiments on a variety of programs using arrays and pointers (including several sorting algorithms) demonstrate the feasibility of the approach on challenging examples. 1.