Program Synthesis and Linear Operator Semantics

For deterministic and probabilistic programs we investigate the problem of program synthesis and program optimisation (with respect to non-functional properties) in the general setting of global optimisation. This approach is based on the representation of the semantics of programs and program fragments in terms of linear operators, i.e. as matrices. We exploit in particular the fact that we can automatically generate the representation of the semantics of elementary blocks. These can then can be used in order to compositionally assemble the semantics of a whole program, i.e. the generator of the corresponding Discrete Time Markov Chain (DTMC). We also utilise a generalised version of Abstract Interpretation suitable for this linear algebraic or functional analytical framework in order to formulate semantical constraints (invariants) and optimisation objectives (for example performance requirements).Comment: In Proceedings SYNT 2014, arXiv:1407.493

Probabilistic data flow analysis: a linear equational approach

Speculative optimisation relies on the estimation of the probabilities that certain properties of the control flow are fulfilled. Concrete or estimated branch probabilities can be used for searching and constructing advantageous speculative and bookkeeping transformations. We present a probabilistic extension of the classical equational approach to data-flow analysis that can be used to this purpose. More precisely, we show how the probabilistic information introduced in a control flow graph by branch prediction can be used to extract a system of linear equations from a program and present a method for calculating correct (numerical) solutions.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Weak Markovian Bisimulation Congruences and Exact CTMC-Level Aggregations for Concurrent Processes

We have recently defined a weak Markovian bisimulation equivalence in an integrated-time setting, which reduces sequences of exponentially timed internal actions to individual exponentially timed internal actions having the same average duration and execution probability as the corresponding sequences. This weak Markovian bisimulation equivalence is a congruence for sequential processes with abstraction and turns out to induce an exact CTMC-level aggregation at steady state for all the considered processes. However, it is not a congruence with respect to parallel composition. In this paper, we show how to generalize the equivalence in a way that a reasonable tradeoff among abstraction, compositionality, and exactness is achieved for concurrent processes. We will see that, by enhancing the abstraction capability in the presence of concurrent computations, it is possible to retrieve the congruence property with respect to parallel composition, with the resulting CTMC-level aggregation being exact at steady state only for a certain subset of the considered processes.Comment: In Proceedings QAPL 2012, arXiv:1207.055

Exact Learning with Tunable Quantum Neural Networks and a Quantum Example Oracle

In this paper, we study the tunable quantum neural network architecture in the quantum exact learning framework with access to a uniform quantum example oracle. We present an approach that uses amplitude amplification to correctly tune the network to the target concept. We applied our approach to the class of positive $k$-juntas and found that $O(n^22^k)$ quantum examples are sufficient with experimental results seemingly showing that a tighter upper bound is possible

Probabilistic Confinement in a Declarative Framework

n/

Tunable Quantum Neural Networks in the QPAC-Learning Framework

In this paper, we investigate the performances of tunable quantum neural networks in the Quantum Probably Approximately Correct (QPAC) learning framework. Tunable neural networks are quantum circuits made of multi-controlled X gates. By tuning the set of controls these circuits are able to approximate any Boolean functions. This architecture is particularly suited to be used in the QPAC-learning framework as it can handle the superposition produced by the oracle. In order to tune the network so that it can approximate a target concept, we have devised and implemented an algorithm based on amplitude amplification. The numerical results show that this approach can efficiently learn concepts from a simple class

Quantitative Aspects of Programming Languages and Systems (2011–12)

n/

Linear Embedding for a Quantitative Comparison of Language Expressiveness

Abstract We introduce the notion of linear embedding which refines Shapiro's notion of embedding by recasting it in a linear-space based semantics setting. We use this notion to compare the expressiveness of a class of languages that employ asynchronous communication primitives a la Linda. The adoption of a linear semantics in which the observables of a language are linear operators (matrices) representing the programs transition graphs allows us to give quantitative estimates of the different expressive power of languages, thus improving previous results in the field