1,471 research outputs found
Linear-time algorithms for testing the satisfiability of propositional horn formulae
AbstractNew algorithms for deciding whether a (propositional) Horn formula is satisfiable are presented. If the Horn formula A contains K distinct propositional letters and if it is assumed that they are exactly P1,…, PK, the two algorithms presented in this paper run in time O(N), where N is the total number of occurrences of literals in A. By representing a Horn proposition as a graph, the satisfiability problem can be formulated as a data flow problem, a certain type of pebbling. The difference between the two algorithms presented here is the strategy used for pebbling the graph. The first algorithm is based on the principle used for finding the set of nonterminals of a context-free grammar from which the empty string can be derived. The second algorithm is a graph traversal and uses a “call-by-need” strategy. This algorithm uses an attribute grammar to translate a propositional Horn formula to its corresponding graph in linear time. Our formulation of the satisfiability problem as a data flow problem appears to be new and suggests the possibility of improving efficiency using parallel processors
Applying Formal Methods to Networking: Theory, Techniques and Applications
Despite its great importance, modern network infrastructure is remarkable for
the lack of rigor in its engineering. The Internet which began as a research
experiment was never designed to handle the users and applications it hosts
today. The lack of formalization of the Internet architecture meant limited
abstractions and modularity, especially for the control and management planes,
thus requiring for every new need a new protocol built from scratch. This led
to an unwieldy ossified Internet architecture resistant to any attempts at
formal verification, and an Internet culture where expediency and pragmatism
are favored over formal correctness. Fortunately, recent work in the space of
clean slate Internet design---especially, the software defined networking (SDN)
paradigm---offers the Internet community another chance to develop the right
kind of architecture and abstractions. This has also led to a great resurgence
in interest of applying formal methods to specification, verification, and
synthesis of networking protocols and applications. In this paper, we present a
self-contained tutorial of the formidable amount of work that has been done in
formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial
On Tackling the Limits of Resolution in SAT Solving
The practical success of Boolean Satisfiability (SAT) solvers stems from the
CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a
propositional proof complexity perspective, CDCL is no more powerful than the
resolution proof system, for which many hard examples exist. This paper
proposes a new problem transformation, which enables reducing the decision
problem for formulas in conjunctive normal form (CNF) to the problem of solving
maximum satisfiability over Horn formulas. Given the new transformation, the
paper proves a polynomial bound on the number of MaxSAT resolution steps for
pigeonhole formulas. This result is in clear contrast with earlier results on
the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper
also establishes the same polynomial bound in the case of modern core-guided
MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard
for CDCL SAT solvers, show that these can be efficiently solved with modern
MaxSAT solvers
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