10 research outputs found
Preface
Overview of the contents of "Foundations of Software Science and Computational Structures: Selected papers from FOSSACS 2005
Beyond Language Equivalence on Visibly Pushdown Automata
We study (bi)simulation-like preorder/equivalence checking on the class of
visibly pushdown automata and its natural subclasses visibly BPA (Basic Process
Algebra) and visibly one-counter automata. We describe generic methods for
proving complexity upper and lower bounds for a number of studied preorders and
equivalences like simulation, completed simulation, ready simulation, 2-nested
simulation preorders/equivalences and bisimulation equivalence. Our main
results are that all the mentioned equivalences and preorders are
EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly
one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for
visibly one-counter automata improves also the previously known DP-hardness
results for ordinary one-counter automata and one-counter nets. Finally, we
study regularity checking problems for visibly pushdown automata and show that
they can be decided in polynomial time.Comment: Final version of paper, accepted by LMC
On the Learnability of Programming Language Semantics
This is the final version of the article. Available from ICE via the DOI in this record.Game semantics is a powerful method of semantic analysis for programming languages. It gives mathematically accurate models ("fully abstract") for a wide variety of programming languages. Game semantic models are combinatorial characterisations of all possible interactions between a term and its syntactic context. Because such interactions can be concretely represented as sets of sequences, it is possible to ask whether they can be learned from examples. Concretely, we are using long short-term memory neural nets (LSTM), a technique which proved effective in learning natural languages for automatic translation and text synthesis, to learn game-semantic models of sequential and concurrent versions of Idealised Algol (IA), which are algorithmically complex yet can be concisely described. We will measure how accurate the learned models are as a function of the degree of the term and the number of free variables involved. Finally, we will show how to use the learned model to perform latent semantic analysis between concurrent and sequential Idealised Algol
On the Learnability of Programming Language Semantics
Game semantics is a powerful method of semantic analysis for programming
languages. It gives mathematically accurate models ("fully abstract") for a
wide variety of programming languages. Game semantic models are combinatorial
characterisations of all possible interactions between a term and its syntactic
context. Because such interactions can be concretely represented as sets of
sequences, it is possible to ask whether they can be learned from examples.
Concretely, we are using long short-term memory neural nets (LSTM), a technique
which proved effective in learning natural languages for automatic translation
and text synthesis, to learn game-semantic models of sequential and concurrent
versions of Idealised Algol (IA), which are algorithmically complex yet can be
concisely described. We will measure how accurate the learned models are as a
function of the degree of the term and the number of free variables involved.
Finally, we will show how to use the learned model to perform latent semantic
analysis between concurrent and sequential Idealised Algol.Comment: In Proceedings ICE 2017, arXiv:1711.1070
Decidability and syntactic control of interference
AbstractWe investigate the decidability of observational equivalence and approximation in Reynolds’ “Syntactic Control of Interference” (SCI), a prototypical functional-imperative language in which covert interference between functions and their arguments is prevented by the use of an affine typing discipline.By associating denotations of terms in a fully abstract “relational” model of finitary basic SCI (due to Reddy) with multitape finite state automata, we show that observational approximation is not decidable (even at first order), but that observational equivalence is decidable for all terms.We then consider the same problems for basic SCI extended with non-local control in the form of backwards jumps. We show that both observational approximation and observational equivalence are decidable in this “observably sequential” version of the language by describing a fully abstract games model in which strategies are regular languages
Third-order Idealized Algol with iteration is decidable
The problems of contextual equivalence and approximation are studied for the third-order fragment of Idealized Algol with iteration (IA*3). They are approached via a combination of game semantics and language theory. It is shown that for each IA*3-term one can construct a pushdown automaton recognizing a representation of the strategy induced by the term. The automata have some additional properties ensuring that the associated equivalence and inclusion problems are solvable in PTIME. This gives an EXPTIME decision procedure for the problems of contextual equivalence and approximation for beta -normal terms. EXPTIME-hardness of the problems, even for terms without iteration, is also shown.Copyright 2007 Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0
The Safe Lambda Calculus
Safety is a syntactic condition of higher-order grammars that constrains
occurrences of variables in the production rules according to their
type-theoretic order. In this paper, we introduce the safe lambda calculus,
which is obtained by transposing (and generalizing) the safety condition to the
setting of the simply-typed lambda calculus. In contrast to the original
definition of safety, our calculus does not constrain types (to be
homogeneous). We show that in the safe lambda calculus, there is no need to
rename bound variables when performing substitution, as variable capture is
guaranteed not to happen. We also propose an adequate notion of beta-reduction
that preserves safety. In the same vein as Schwichtenberg's 1976
characterization of the simply-typed lambda calculus, we show that the numeric
functions representable in the safe lambda calculus are exactly the
multivariate polynomials; thus conditional is not definable. We also give a
characterization of representable word functions. We then study the complexity
of deciding beta-eta equality of two safe simply-typed terms and show that this
problem is PSPACE-hard. Finally we give a game-semantic analysis of safety: We
show that safe terms are denoted by `P-incrementally justified strategies'.
Consequently pointers in the game semantics of safe lambda-terms are only
necessary from order 4 onwards
Thin Games with Symmetry and Concurrent Hyland-Ong Games
We build a cartesian closed category, called Cho, based on event structures.
It allows an interpretation of higher-order stateful concurrent programs that
is refined and precise: on the one hand it is conservative with respect to
standard Hyland-Ong games when interpreting purely functional programs as
innocent strategies, while on the other hand it is much more expressive. The
interpretation of programs constructs compositionally a representation of their
execution that exhibits causal dependencies and remembers the points of
non-deterministic branching.The construction is in two stages. First, we build
a compact closed category Tcg. It is a variant of Rideau and Winskel's category
CG, with the difference that games and strategies in Tcg are equipped with
symmetry to express that certain events are essentially the same. This is
analogous to the underlying category of AJM games enriching simple games with
an equivalence relations on plays. Building on this category, we construct the
cartesian closed category Cho as having as objects the standard arenas of
Hyland-Ong games, with strategies, represented by certain events structures,
playing on games with symmetry obtained as expanded forms of these arenas.To
illustrate and give an operational light on these constructions, we interpret
(a close variant of) Idealized Parallel Algol in Cho