1,157 research outputs found
A Theory of Formal Synthesis via Inductive Learning
Formal synthesis is the process of generating a program satisfying a
high-level formal specification. In recent times, effective formal synthesis
methods have been proposed based on the use of inductive learning. We refer to
this class of methods that learn programs from examples as formal inductive
synthesis. In this paper, we present a theoretical framework for formal
inductive synthesis. We discuss how formal inductive synthesis differs from
traditional machine learning. We then describe oracle-guided inductive
synthesis (OGIS), a framework that captures a family of synthesizers that
operate by iteratively querying an oracle. An instance of OGIS that has had
much practical impact is counterexample-guided inductive synthesis (CEGIS). We
present a theoretical characterization of CEGIS for learning any program that
computes a recursive language. In particular, we analyze the relative power of
CEGIS variants where the types of counterexamples generated by the oracle
varies. We also consider the impact of bounded versus unbounded memory
available to the learning algorithm. In the special case where the universe of
candidate programs is finite, we relate the speed of convergence to the notion
of teaching dimension studied in machine learning theory. Altogether, the
results of the paper take a first step towards a theoretical foundation for the
emerging field of formal inductive synthesis
Process Algebras
Process Algebras are mathematically rigorous languages with well defined semantics that permit describing and verifying properties of concurrent communicating systems.
They can be seen as models of processes, regarded as agents that act and interact continuously with other similar agents and with their common environment. The agents may be real-world objects (even people), or they may be artifacts, embodied perhaps in computer hardware or software systems.
Many different approaches (operational, denotational, algebraic) are taken for describing the meaning of processes. However, the operational approach is the reference one. By relying on the so called Structural Operational Semantics (SOS), labelled transition systems are built and composed by using the different operators of the many different process algebras. Behavioral equivalences are used to abstract from unwanted details and identify those systems that react similarly to external
experiments
A formal model of asynchronous communication and its use in mechanically verifying a biphase mark protocol
In this paper we present a formal model of asynchronous communication as a function in the Boyer-Moore logic. The function transforms the signal stream generated by one processor into the signal stream consumed by an independently clocked processor. This transformation 'blurs' edges and 'dilates' time due to differences in the phases and rates of the two clocks and the communications delay. The model can be used quantitatively to derive concrete performance bounds on asynchronous communications at ISO protocol level 1 (physical level). We develop part of the reusable formal theory that permits the convenient application of the model. We use the theory to show that a biphase mark protocol can be used to send messages of arbitrary length between two asynchronous processors. We study two versions of the protocol, a conventional one which uses cells of size 32 cycles and an unconventional one which uses cells of size 18. We conjecture that the protocol can be proved to work under our model for smaller cell sizes and more divergent clock rates but the proofs would be harder
A Linear First-Order Functional Intermediate Language for Verified Compilers
We present the linear first-order intermediate language IL for verified
compilers. IL is a functional language with calls to a nondeterministic
environment. We give IL terms a second, imperative semantic interpretation and
obtain a register transfer language. For the imperative interpretation we
establish a notion of live variables. Based on live variables, we formulate a
decidable property called coherence ensuring that the functional and the
imperative interpretation of a term coincide. We formulate a register
assignment algorithm for IL and prove its correctness. The algorithm translates
a functional IL program into an equivalent imperative IL program. Correctness
follows from the fact that the algorithm reaches a coherent program after
consistently renaming local variables. We prove that the maximal number of live
variables in the initial program bounds the number of different variables in
the final coherent program. The entire development is formalized in Coq.Comment: Addressed comments from reviewers (ITP 2015): (1) Added discussion of
a paper in related work (2) Added definition of renamed-apart in appendix (3)
Formulation changes in a coupe of place
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