Theory and Techniques for Synthesizing a Family of Graph Algorithms

Although Breadth-First Search (BFS) has several advantages over Depth-First Search (DFS) its prohibitive space requirements have meant that algorithm designers often pass it over in favor of DFS. To address this shortcoming, we introduce a theory of Efficient BFS (EBFS) along with a simple recursive program schema for carrying out the search. The theory is based on dominance relations, a long standing technique from the field of search algorithms. We show how the theory can be used to systematically derive solutions to two graph algorithms, namely the Single Source Shortest Path problem and the Minimum Spanning Tree problem. The solutions are found by making small systematic changes to the derivation, revealing the connections between the two problems which are often obscured in textbook presentations of them.Comment: In Proceedings SYNT 2012, arXiv:1207.055

Time Line of the Brady Shootout

A brief time line of the events leading up to and including the shoot out in Bangor, Maine, on October 12, 1937.https://digicom.bpl.lib.me.us/spc_brady_bk/1001/thumbnail.jp

Binary-Compatible Verification of Filesystems with ACL2

Filesystems are an essential component of most computer systems. Work on the verification of filesystem functionality has been focused on constructing new filesystems in a manner which simplifies the process of verifying them against specifications. This leaves open the question of whether filesystems already in use are correct at the binary level. This paper introduces LoFAT, a model of the FAT32 filesystem which efficiently implements a subset of the POSIX filesystem operations, and HiFAT, a more abstract model of FAT32 which is simpler to reason about. LoFAT is proved to be correct in terms of refinement of HiFAT, and made executable by enabling the state of the model to be written to and read from FAT32 disk images. EqFAT, an equivalence relation for disk images, considers whether two disk images contain the same directory tree modulo reordering of files and implementation-level details regarding cluster allocation. A suite of co-simulation tests uses EqFAT to compare the operation of existing FAT32 implementations to LoFAT and check the correctness of existing implementations of FAT32 such as the mtools suite of programs and the Linux FAT32 implementation. All models and proofs are formalized and mechanically verified in ACL2

Computer Studies Of Neurophysiological And Psychological Events

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/116309/1/nyas00059.pd

Synthesis of Greedy Algorithms Using Dominance Relations

Greedy algorithms exploit problem structure and constraints to achieve linear-time performance. Yet there is still no completely satisfactory way of constructing greedy algorithms. For example, the Greedy Algorithm of Edmonds depends upon translating a problem into an algebraic structure called a matroid, but the existence of such a translation can be as hard to determine as the existence of a greedy algorithm itself. An alternative characterization of greedy algorithms is in terms of dominance relations, a well-known algorithmic technique used to prune search spaces. We demonstrate a process by which dominance relations can be methodically derived for a number of greedy algorithms, including activity selection, and prefix-free codes. By incorporating our approach into an existing framework for algorithm synthesis, we demonstrate that it could be the basis for an effective engineering method for greedy algorithms. We also compare our approach with other characterizations of greedy algorithms

Tactical Synthesis Of Efficient Global Search Algorithms

Algorithm synthesis transforms a formal specification into an efficient algorithm to solve a problem. Algorithm synthesis in Specware combines the formal specification of a problem with a high-level algorithm strategy. To derive an efficient algorithm, a developer must define operators that refine the algorithm by combining the generic operators in the algorithm with the details of the problem specification. This derivation requires skill and a deep understanding of the problem and the algorithmic strategy. In this paper we introduce two tactics to ease this process. The tactics serve a similar purpose to tactics used for determining indefinite integrals in calculus, that is suggesting possible ways to attack the problem

The design and implementation of Object Grammars

An Object Grammar is a variation on traditional BNF grammars, where the notation is extended to support declarative bidirectional mappings between text and object graphs. The two directions for interpreting Object Grammars are parsing and formatting. Parsing transforms text into an object graph by recognizing syntactic features and creating the corresponding object structure. In the reverse direction, formatting recognizes object graph features and generates an appropriate textual presentation. The key to Object Grammars is the expressive power of the mapping, which decouples the syntactic structure from the graph structure. To handle graphs, Object Grammars support declarative annotations for resolving textual names that refer to arbitrary objects in the graph structure. Predicates on the semantic structure provide additional control over the mapping. Furthermore, Object Grammars are compositional so that languages may be defined in a modular fashion. We have implemented our approach to Object Grammars as one of the foundations of the Ens (o) over bar system and illustrate the utility of our approach by showing how it enables definition and composition of domain-specific languages (DSLs). (C) 2014 Elsevier B.V. All rights reserved.</p