2,015 research outputs found
Towards Verifying Nonlinear Integer Arithmetic
We eliminate a key roadblock to efficient verification of nonlinear integer
arithmetic using CDCL SAT solvers, by showing how to construct short resolution
proofs for many properties of the most widely used multiplier circuits. Such
short proofs were conjectured not to exist. More precisely, we give n^{O(1)}
size regular resolution proofs for arbitrary degree 2 identities on array,
diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs
for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result
Formal Proof of SCHUR Conjugate Function
The main goal of our work is to formally prove the correctness of the key
commands of the SCHUR software, an interactive program for calculating with
characters of Lie groups and symmetric functions. The core of the computations
relies on enumeration and manipulation of combinatorial structures. As a first
"proof of concept", we present a formal proof of the conjugate function,
written in C. This function computes the conjugate of an integer partition. To
formally prove this program, we use the Frama-C software. It allows us to
annotate C functions and to generate proof obligations, which are proved using
several automated theorem provers. In this paper, we also draw on methodology,
discussing on how to formally prove this kind of program.Comment: To appear in CALCULEMUS 201
Modal ”-Calculus, Model Checking and Gauà Elimination
In this paper we present a novel approach for solving Boolean equation systems with nested minimal and maximal fixpoints. The method works by successively eliminating variables and reducing a Boolean equation system similar to GauĂ elimination for linear equation systems. It does not require backtracking techniques. Within one framework we suggest a global and a local algorithm. In the context of model checking in the modal-calculus the local algorithm is related to the tableau methods, but has a better worst case complexity
LangPro: Natural Language Theorem Prover
LangPro is an automated theorem prover for natural language
(https://github.com/kovvalsky/LangPro). Given a set of premises and a
hypothesis, it is able to prove semantic relations between them. The prover is
based on a version of analytic tableau method specially designed for natural
logic. The proof procedure operates on logical forms that preserve linguistic
expressions to a large extent. %This property makes the logical forms easily
obtainable from syntactic trees. %, in particular, Combinatory Categorial
Grammar derivation trees. The nature of proofs is deductive and transparent. On
the FraCaS and SICK textual entailment datasets, the prover achieves high
results comparable to state-of-the-art.Comment: 6 pages, 8 figures, Conference on Empirical Methods in Natural
Language Processing (EMNLP) 201
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