13,949 research outputs found
Incremental branching programs
We propose a new model of restricted branching programs
which we call {em incremental branching programs}.
We show that {em syntactic}
incremental branching programs capture previously studied
structured models of computation for the problem GEN, namely marking
machines [Cook74].
and Poon\u27s extension [Poon93] of jumping automata
on graphs [CookRackoff80].
We then prove
exponential size lower bounds for our syntactic incremental model,
and for some other restricted branching program models as well.
We further show that nondeterministic syntactic incremental
branching programs are
provably stronger than their deterministic counterpart when solving a
natural NL-complete GEN subproblem.
It remains open if syntactic incremental branching programs are as powerful
as unrestricted branching programs for GEN problems.
Joint work with Anna Gál and Michal KouckÃ
EXTREMELY UNIFORM BRANCHING PROGRAMS
We propose a new descriptive complexity notion of uniformity for branching programs solving problems defined on structured data. We observe that FO[=]-uniform (n-way) branching programs are unable to solve the tree evaluation problem studied by Cook, McKenzie, Wehr, Braverman and Santhanam [8] because such programs possess a variant of their thriftiness property. Similarly, FO[=]-uniform (n-way) branching programs are unable to solve the P-complete GEN problem because such programs possess the incremental property studied by Gál, Kouck´y and McKenzie [10]. 1
Pebbling, Entropy and Branching Program Size Lower Bounds
We contribute to the program of proving lower bounds on the size of branching
programs solving the Tree Evaluation Problem introduced by Cook et. al. (2012).
Proving a super-polynomial lower bound for the size of nondeterministic thrifty
branching programs (NTBP) would separate from for thrifty models
solving the tree evaluation problem. First, we show that {\em Read-Once NTBPs}
are equivalent to whole black-white pebbling algorithms thus showing a tight
lower bound (ignoring polynomial factors) for this model.
We then introduce a weaker restriction of NTBPs called {\em Bitwise
Independence}. The best known NTBPs (of size ) for the tree
evaluation problem given by Cook et. al. (2012) are Bitwise Independent. As our
main result, we show that any Bitwise Independent NTBP solving
must have at least states. Prior to this work, lower
bounds were known for NTBPs only for fixed heights (See Cook et. al.
(2012)). We prove our results by associating a fractional black-white pebbling
strategy with any bitwise independent NTBP solving the Tree Evaluation Problem.
Such a connection was not known previously even for fixed heights.
Our main technique is the entropy method introduced by Jukna and Z{\'a}k
(2001) originally in the context of proving lower bounds for read-once
branching programs. We also show that the previous lower bounds given by Cook
et. al. (2012) for deterministic branching programs for Tree Evaluation Problem
can be obtained using this approach. Using this method, we also show tight
lower bounds for any -way deterministic branching program solving Tree
Evaluation Problem when the instances are restricted to have the same group
operation in all internal nodes.Comment: 25 Pages, Manuscript submitted to Journal in June 2013 This version
includes a proof for tight size bounds for (syntactic) read-once NTBPs. The
proof is in the same spirit as the proof for size bounds for bitwise
independent NTBPs present in the earlier version of the paper and is included
in the journal version of the paper submitted in June 201
Improving the Asymmetric TSP by Considering Graph Structure
Recent works on cost based relaxations have improved Constraint Programming
(CP) models for the Traveling Salesman Problem (TSP). We provide a short survey
over solving asymmetric TSP with CP. Then, we suggest new implied propagators
based on general graph properties. We experimentally show that such implied
propagators bring robustness to pathological instances and highlight the fact
that graph structure can significantly improve search heuristics behavior.
Finally, we show that our approach outperforms current state of the art
results.Comment: Technical repor
Rich Counter-Examples for Temporal-Epistemic Logic Model Checking
Model checking verifies that a model of a system satisfies a given property,
and otherwise produces a counter-example explaining the violation. The verified
properties are formally expressed in temporal logics. Some temporal logics,
such as CTL, are branching: they allow to express facts about the whole
computation tree of the model, rather than on each single linear computation.
This branching aspect is even more critical when dealing with multi-modal
logics, i.e. logics expressing facts about systems with several transition
relations. A prominent example is CTLK, a logic that reasons about temporal and
epistemic properties of multi-agent systems. In general, model checkers produce
linear counter-examples for failed properties, composed of a single computation
path of the model. But some branching properties are only poorly and partially
explained by a linear counter-example.
This paper proposes richer counter-example structures called tree-like
annotated counter-examples (TLACEs), for properties in Action-Restricted CTL
(ARCTL), an extension of CTL quantifying paths restricted in terms of actions
labeling transitions of the model. These counter-examples have a branching
structure that supports more complete description of property violations.
Elements of these counter-examples are annotated with parts of the property to
give a better understanding of their structure. Visualization and browsing of
these richer counter-examples become a critical issue, as the number of
branches and states can grow exponentially for deeply-nested properties.
This paper formally defines the structure of TLACEs, characterizes adequate
counter-examples w.r.t. models and failed properties, and gives a generation
algorithm for ARCTL properties. It also illustrates the approach with examples
in CTLK, using a reduction of CTLK to ARCTL. The proposed approach has been
implemented, first by extending the NuSMV model checker to generate and export
branching counter-examples, secondly by providing an interactive graphical
interface to visualize and browse them.Comment: In Proceedings IWIGP 2012, arXiv:1202.422
Symbolic Execution as DPLL Modulo Theories
© Quoc-Sang Phan; licensed under Creative Commons License CC-BY. Imperial College Computing Student Workshop (ICCSW’14). Editors: Rumyana Neykova and Nicholas Ng; pp. 58–65. OpenAccess Series in Informatics. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germanyurn: urn:nbn:de:0030-drops-47746urn: urn:nbn:de:0030-drops-4774
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