2,922 research outputs found
SMT-Based Bounded Model Checking of Fixed-Point Digital Controllers
Digital controllers have several advantages with respect to their flexibility
and design's simplicity. However, they are subject to problems that are not
faced by analog controllers. In particular, these problems are related to the
finite word-length implementation that might lead to overflows, limit cycles,
and time constraints in fixed-point processors. This paper proposes a new
method to detect design's errors in digital controllers using a state-of-the
art bounded model checker based on satisfiability modulo theories. The
experiments with digital controllers for a ball and beam plant demonstrate that
the proposed method can be very effective in finding errors in digital
controllers than other existing approaches based on traditional simulations
tools
Delta-Complete Decision Procedures for Satisfiability over the Reals
We introduce the notion of "\delta-complete decision procedures" for solving
SMT problems over the real numbers, with the aim of handling a wide range of
nonlinear functions including transcendental functions and solutions of
Lipschitz-continuous ODEs. Given an SMT problem \varphi and a positive rational
number \delta, a \delta-complete decision procedure determines either that
\varphi is unsatisfiable, or that the "\delta-weakening" of \varphi is
satisfiable. Here, the \delta-weakening of \varphi is a variant of \varphi that
allows \delta-bounded numerical perturbations on \varphi. We prove the
existence of \delta-complete decision procedures for bounded SMT over reals
with functions mentioned above. For functions in Type 2 complexity class C,
under mild assumptions, the bounded \delta-SMT problem is in NP^C.
\delta-Complete decision procedures can exploit scalable numerical methods for
handling nonlinearity, and we propose to use this notion as an ideal
requirement for numerically-driven decision procedures. As a concrete example,
we formally analyze the DPLL framework, which integrates Interval
Constraint Propagation (ICP) in DPLL(T), and establish necessary and sufficient
conditions for its \delta-completeness. We discuss practical applications of
\delta-complete decision procedures for correctness-critical applications
including formal verification and theorem proving.Comment: A shorter version appears in IJCAR 201
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