The Tree Width of Separation Logic with Recursive Definitions

Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current results report on techniques to decide satisfiability and validity of entailments for Separation Logic(s) over lists (possibly with data). In this paper we establish a more general decidability result. We prove that any Separation Logic formula using rather general recursively defined predicates is decidable for satisfiability, and moreover, entailments between such formulae are decidable for validity. These predicates are general enough to define (doubly-) linked lists, trees, and structures more general than trees, such as trees whose leaves are chained in a list. The decidability proofs are by reduction to decidability of Monadic Second Order Logic on graphs with bounded tree width.Comment: 30 pages, 2 figure

The Complexity of Repairing, Adjusting, and Aggregating of Extensions in Abstract Argumentation

We study the computational complexity of problems that arise in abstract argumentation in the context of dynamic argumentation, minimal change, and aggregation. In particular, we consider the following problems where always an argumentation framework F and a small positive integer k are given. - The Repair problem asks whether a given set of arguments can be modified into an extension by at most k elementary changes (i.e., the extension is of distance k from the given set). - The Adjust problem asks whether a given extension can be modified by at most k elementary changes into an extension that contains a specified argument. - The Center problem asks whether, given two extensions of distance k, whether there is a "center" extension that is a distance at most (k-1) from both given extensions. We study these problems in the framework of parameterized complexity, and take the distance k as the parameter. Our results covers several different semantics, including admissible, complete, preferred, semi-stable and stable semantics

Synaptic abnormalities in the infralimbic cortex of a model of congenital depression

Multiple lines of evidence suggest that disturbances in excitatory transmission contribute to depression. Whether these defects involve the number, size, or composition of glutamatergic contacts is unclear. This study used recently introduced procedures for fluorescence deconvolution tomography in a well-studied rat model of congenital depression to characterize excitatory synapses in layer I of infralimbic cortex, a region involved in mood disorders, and of primary somatosensory cortex. Three groups were studied: (1) rats bred for learned helplessness (cLH); (2) rats resistant to learned helplessness (cNLH); and (3) control Sprague Dawley rats. In fields within infralimbic cortex, cLH rats had the same numerical density of synapses, immunolabeled for either the postsynaptic density (PSD) marker PSD95 or the presynaptic protein synaptophysin, as controls. However, PSD95 immunolabeling intensities were substantially lower in cLH rats, as were numerical densities of synapse-sized clusters of the AMPA receptor subunit GluA1. Similar but less pronounced differences (comparable numerical densities but reduced immunolabeling intensity for PSD95) were found in the somatosensory cortex. In contrast, non-helpless rats had 25% more PSDs than either cLH or control rats without any increase in synaptophysin-labeled terminal frequency. Compared with controls, both cLH and cNLH rats had fewer GABAergic contacts. These results indicate that congenital tendencies that increase or decrease depression-like behavior differentially affect excitatory synapses

On the Monadic Second-Order Transduction Hierarchy

We compare classes of finite relational structures via monadic second-order transductions. More precisely, we study the preorder where we set C \subseteq K if, and only if, there exists a transduction {\tau} such that C\subseteq{\tau}(K). If we only consider classes of incidence structures we can completely describe the resulting hierarchy. It is linear of order type {\omega}+3. Each level can be characterised in terms of a suitable variant of tree-width. Canonical representatives of the various levels are: the class of all trees of height n, for each n \in N, of all paths, of all trees, and of all grids

Compact Labelings For Efficient First-Order Model-Checking

We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of every class that is \emph{nicely locally cwd-decomposable}. This notion generalizes that of a \emph{nicely locally tree-decomposable} class. The graphs of such classes can be covered by graphs of bounded \emph{clique-width} with limited overlaps. We also consider such labelings for \emph{bounded} first-order formulas on graph classes of \emph{bounded expansion}. Some of these results are extended to counting queries

The Grizzly, April 15, 1983

Second Attack: Improvements Sought for Security • New Senior Fund • Seminar Planned • The A\u27s Come to Helfferich Hall • Letter to the Editor: Most Abominable Act • Faculty Promotions Approved • President\u27s Corner • Sexual Assault in Quad • Security Tips • Nuclear Freeze Concert • Ursinus Representatives at UN • Ice Cream Night at Bear\u27s Den • Final Exam Schedule • Republicans for Rock! • Escape From Ursinus • Bear Batsmen Drop Slugfest • Men\u27s Track Evens Up • Men\u27s Tennis Nets Two Wins • Girls\u27 Nets Optimistic • Men\u27s Lacrosse Victorioushttps://digitalcommons.ursinus.edu/grizzlynews/1098/thumbnail.jp

Packing and covering immersion models of planar subcubic graphs

A graph $H$ is an immersion of a graph $G$ if $H$ can be obtained by some sugraph $G$ after lifting incident edges. We prove that there is a polynomial function $f:\Bbb{N}\times\Bbb{N}\rightarrow\Bbb{N}$, such that if $H$ is a connected planar subcubic graph on $h>0$ edges, $G$ is a graph, and $k$ is a non-negative integer, then either $G$ contains $k$ vertex/edge-disjoint subgraphs, each containing $H$ as an immersion, or $G$ contains a set $F$ of $f(k,h)$ vertices/edges such that $G\setminus F$ does not contain $H$ as an immersion

The Grizzly, March 25, 1983

New Editors Elected: Romer, Hong, Pasekoff Named • Superstars Tournament Needs Participants • DuPont Gives Third Consecutive Chemistry Grant • The A\u27s Come to UC • Third Annual Special Olympics This Weekend • Summer in Japan • Folk Singers at Bomberger • Letters to the Editor: An Epilogue to Zeta Chi • USGA Holds Election • USGA Notes • Voight at Bat • 13 Spend Break in Quebec • To Hell With the USFL • College Bowl Goes to Maryland • 1983 Room Selection Procedure • Bear\u27s Den Replaces Cafe International • Cycling Marathon: Ride for Your Life • Men\u27s Lacrosse Slow Getting Started • Men\u27s and Women\u27s Track Win Openershttps://digitalcommons.ursinus.edu/grizzlynews/1097/thumbnail.jp

The Grizzly, March 4, 1983

Zeta Chi Suspended: Fraternity Disciplined for Pledging Violations • Symposium Topics Discussed • New Forum Committee to Revise System • Letters to the Editor: Alumnus Responds to Grizzly Policy • Committee Reviews Appeals Procedure • Meistersingers Tour • Exam Schedule • Woodcuts at Myrin • Stravinsky Program Ends Winterfest • Lantern Deadline Approaches • Lewis on Wall Street • Alpha Sigma Nu Tops GPAs • Roving Reporter: The Administration is Proposing to put a Live-in Dean in 97 of New Men\u27s Dorm • Pre-Legal Society Resurrected • Swimmers Perform Beyond Expectation • Bear Blades Blaze to Victory • Gymnasts Draw No. 2 Ratinghttps://digitalcommons.ursinus.edu/grizzlynews/1096/thumbnail.jp