Benjamin Rossman

Learn More
The Abstract State Machine Language, AsmL, is a novel executable specification language based on the theory of Abstract State Machines. AsmL is object-oriented, provides high-level mathematical data-structures, and is built around the notion of synchronous updates and finite choice. AsmL is fully integrated into the .NET framework and Microsoft development(More)
The <i>edit distance</i> between two ordered rooted trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this article, we present a worst-case <i>O</i>(<i>n</i><sup>3</sup>)-time algorithm for the(More)
The homomorphism preservation theorem (h.p.t.), a result in classical model theory, states that a first-order formula is preserved under homomorphisms on all structures (finite and infinite) if and only if it is equivalent to an existential-positive formula. Answering a long-standing question in finite model theory, we prove that the h.p.t. remains valid(More)
We prove a lower bound of &#969;(n<sup>k/4</sup>) on the size of constant-depth circuits solving the k-clique problem on n-vertex graphs (for every constant k). This improves a lower bound of &#969;(n<sup>k/89d<sup>2</sup></sup>) due to Beame where d is the circuit depth. Our lower bound has the advantage that it does not depend on the constant d in the(More)
It is widely suspected that Erd\H{o}s-R\'enyi random graphs are a source of hard instances for clique problems. Giving further evidence for this belief, we prove the first average-case hardness result for the $k$-clique problem on monotone circuits. Specifically, we show that no monotone circuit of size $O(n^{k/4})$ solves the $k$-clique problem with high(More)
The computational problem of testing whether a graph contains a complete subgraph of size k is among the most fundamental problems studied in theoretical computer science. This thesis is concerned with proving lower bounds for k-CLIQUE, as this problem is known. Our results show that, in certain models of computation, solving k-CLIQUE in the average case(More)
We prove an average-case depth hierarchy theorem for Boolean circuits over the standard basis of AND, OR, and NOT gates. Our hierarchy theorem says that for every <i>d</i> &#8805; 2, there is an explicit <i>n</i>-variable Boolean function <i>f</i>, computed by a linear-size depth-<i>d</i> formula, which is such that any depth-(<i>d</i>&minus;1) circuit that(More)
We consider Choiceless Polynomial Time (C̃PT), a language introduced by Blass, Gurevich and Shelah, and show that it can express a query originally constructed by Cai, Fürer and Immerman to separate fixed-point logic with counting (IFP + C) from P. This settles a question posed by Blass et al. The program we present uses sets of unbounded finite rank: we(More)