4,981 research outputs found
On the origin of ambiguity in efficient communication
This article studies the emergence of ambiguity in communication through the
concept of logical irreversibility and within the framework of Shannon's
information theory. This leads us to a precise and general expression of the
intuition behind Zipf's vocabulary balance in terms of a symmetry equation
between the complexities of the coding and the decoding processes that imposes
an unavoidable amount of logical uncertainty in natural communication.
Accordingly, the emergence of irreversible computations is required if the
complexities of the coding and the decoding processes are balanced in a
symmetric scenario, which means that the emergence of ambiguous codes is a
necessary condition for natural communication to succeed.Comment: 28 pages, 2 figure
Learning to Prove Theorems via Interacting with Proof Assistants
Humans prove theorems by relying on substantial high-level reasoning and
problem-specific insights. Proof assistants offer a formalism that resembles
human mathematical reasoning, representing theorems in higher-order logic and
proofs as high-level tactics. However, human experts have to construct proofs
manually by entering tactics into the proof assistant. In this paper, we study
the problem of using machine learning to automate the interaction with proof
assistants. We construct CoqGym, a large-scale dataset and learning environment
containing 71K human-written proofs from 123 projects developed with the Coq
proof assistant. We develop ASTactic, a deep learning-based model that
generates tactics as programs in the form of abstract syntax trees (ASTs).
Experiments show that ASTactic trained on CoqGym can generate effective tactics
and can be used to prove new theorems not previously provable by automated
methods. Code is available at https://github.com/princeton-vl/CoqGym.Comment: Accepted to ICML 201
Biologically inspired distributed machine cognition: a new formal approach to hyperparallel computation
The irresistable march toward multiple-core chip technology presents currently intractable pdrogramming challenges. High level mental processes in many animals, and their analogs for social structures, appear similarly massively parallel, and recent mathematical models addressing them may be adaptable to the multi-core programming problem
Prolegomena to an operator theory of computation
Defining computation as information processing (information dynamics) with information as a relational property of data structures (the difference in one system that makes a difference in another system) makes it very suitable to use operator formulation, with similarities to category theory. The concept of the operator is exceedingly important in many knowledge areas as a tool of theoretical studies and practical applications. Here we introduce the operator theory of computing, opening new opportunities for the exploration of computing devices, processes, and their networks
Compositional Verification for Timed Systems Based on Automatic Invariant Generation
We propose a method for compositional verification to address the state space
explosion problem inherent to model-checking timed systems with a large number
of components. The main challenge is to obtain pertinent global timing
constraints from the timings in the components alone. To this end, we make use
of auxiliary clocks to automatically generate new invariants which capture the
constraints induced by the synchronisations between components. The method has
been implemented in the RTD-Finder tool and successfully experimented on
several benchmarks
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