10,646 research outputs found
Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis
Even with impressive advances in automated formal methods, certain problems
in system verification and synthesis remain challenging. Examples include the
verification of quantitative properties of software involving constraints on
timing and energy consumption, and the automatic synthesis of systems from
specifications. The major challenges include environment modeling,
incompleteness in specifications, and the complexity of underlying decision
problems.
This position paper proposes sciduction, an approach to tackle these
challenges by integrating inductive inference, deductive reasoning, and
structure hypotheses. Deductive reasoning, which leads from general rules or
concepts to conclusions about specific problem instances, includes techniques
such as logical inference and constraint solving. Inductive inference, which
generalizes from specific instances to yield a concept, includes algorithmic
learning from examples. Structure hypotheses are used to define the class of
artifacts, such as invariants or program fragments, generated during
verification or synthesis. Sciduction constrains inductive and deductive
reasoning using structure hypotheses, and actively combines inductive and
deductive reasoning: for instance, deductive techniques generate examples for
learning, and inductive reasoning is used to guide the deductive engines.
We illustrate this approach with three applications: (i) timing analysis of
software; (ii) synthesis of loop-free programs, and (iii) controller synthesis
for hybrid systems. Some future applications are also discussed
Spatial Interpolants
We propose Splinter, a new technique for proving properties of
heap-manipulating programs that marries (1) a new separation logic-based
analysis for heap reasoning with (2) an interpolation-based technique for
refining heap-shape invariants with data invariants. Splinter is property
directed, precise, and produces counterexample traces when a property does not
hold. Using the novel notion of spatial interpolants modulo theories, Splinter
can infer complex invariants over general recursive predicates, e.g., of the
form all elements in a linked list are even or a binary tree is sorted.
Furthermore, we treat interpolation as a black box, which gives us the freedom
to encode data manipulation in any suitable theory for a given program (e.g.,
bit vectors, arrays, or linear arithmetic), so that our technique immediately
benefits from any future advances in SMT solving and interpolation.Comment: Short version published in ESOP 201
Reasoned modelling critics: turning failed proofs into modelling guidance
The activities of formal modelling and reasoning are closely related. But while the rigour of building formal models brings significant benefits, formal reasoning remains a major barrier to the wider acceptance of formalism within design. Here we propose reasoned modelling critics â an approach which aims to abstract away from the complexities of low-level proof obligations, and provide high-level modelling guidance to designers when proofs fail. Inspired by proof planning critics, the technique combines proof-failure analysis with modelling heuristics. Here, we present the details of our proposal, implement them in a prototype and outline future plans
Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis
The safety of infinite state systems can be checked by a backward
reachability procedure. For certain classes of systems, it is possible to prove
the termination of the procedure and hence conclude the decidability of the
safety problem. Although backward reachability is property-directed, it can
unnecessarily explore (large) portions of the state space of a system which are
not required to verify the safety property under consideration. To avoid this,
invariants can be used to dramatically prune the search space. Indeed, the
problem is to guess such appropriate invariants. In this paper, we present a
fully declarative and symbolic approach to the mechanization of backward
reachability of infinite state systems manipulating arrays by Satisfiability
Modulo Theories solving. Theories are used to specify the topology and the data
manipulated by the system. We identify sufficient conditions on the theories to
ensure the termination of backward reachability and we show the completeness of
a method for invariant synthesis (obtained as the dual of backward
reachability), again, under suitable hypotheses on the theories. We also
present a pragmatic approach to interleave invariant synthesis and backward
reachability so that a fix-point for the set of backward reachable states is
more easily obtained. Finally, we discuss heuristics that allow us to derive an
implementation of the techniques in the model checker MCMT, showing remarkable
speed-ups on a significant set of safety problems extracted from a variety of
sources.Comment: Accepted for publication in Logical Methods in Computer Scienc
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