1,448 research outputs found
Fifty years of Hoare's Logic
We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin
Linear Time Subgraph Counting, Graph Degeneracy, and the Chasm at Size Six
We consider the problem of counting all k-vertex subgraphs in an input graph, for any constant k. This problem (denoted SUB-CNT_k) has been studied extensively in both theory and practice. In a classic result, Chiba and Nishizeki (SICOMP 85) gave linear time algorithms for clique and 4-cycle counting for bounded degeneracy graphs. This is a rich class of sparse graphs that contains, for example, all minor-free families and preferential attachment graphs. The techniques from this result have inspired a number of recent practical algorithms for SUB-CNT_k. Towards a better understanding of the limits of these techniques, we ask: for what values of k can SUB_CNT_k be solved in linear time?
We discover a chasm at k=6. Specifically, we prove that for k < 6, SUB_CNT_k can be solved in linear time. Assuming a standard conjecture in fine-grained complexity, we prove that for all k ? 6, SUB-CNT_k cannot be solved even in near-linear time
Satisfiability, sequence niches, and molecular codes in cellular signaling
Biological information processing as implemented by regulatory and signaling
networks in living cells requires sufficient specificity of molecular
interaction to distinguish signals from one another, but much of regulation and
signaling involves somewhat fuzzy and promiscuous recognition of molecular
sequences and structures, which can leave systems vulnerable to crosstalk. This
paper examines a simple computational model of protein-protein interactions
which reveals both a sharp onset of crosstalk and a fragmentation of the
neutral network of viable solutions as more proteins compete for regions of
sequence space, revealing intrinsic limits to reliable signaling in the face of
promiscuity. These results suggest connections to both phase transitions in
constraint satisfaction problems and coding theory bounds on the size of
communication codes
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