21 research outputs found
Expressivity Within Second-Order Transitive-Closure Logic
Second-order transitive-closure logic, SO(TC), is an expressive declarative language that captures the complexity class PSPACE. Already its monadic fragment, MSO(TC), allows the expression of various NP-hard and even PSPACE-hard problems in a natural and elegant manner. As SO(TC) offers an attractive framework for expressing properties in terms of declaratively specified computations, it is interesting to understand the expressivity of different features of the language. This paper focuses on the fragment MSO(TC), as well on the purely existential fragment SO(2TC)(exists); in 2TC, the TC operator binds only tuples of relation variables. We establish that, with respect to expressive power, SO(2TC)(exists) collapses to existential first-order logic. In addition we study the relationship of MSO(TC) to an extension of MSO(TC) with counting features (CMSO(TC)) as well as to order-invariant MSO. We show that the expressive powers of CMSO(TC) and MSO(TC) coincide. Moreover we establish that, over unary vocabularies, MSO(TC) strictly subsumes order-invariant MSO
The (In)Efficiency of interaction
Evaluating higher-order functional programs through abstract machines inspired by the geometry of the interaction is known to induce space efficiencies, the price being time performances often poorer than those obtainable with traditional, environment-based, abstract machines. Although families of lambda-terms for which the former is exponentially less efficient than the latter do exist, it is currently unknown how general this phenomenon is, and how far the inefficiencies can go, in the worst case. We answer these questions formulating four different well-known abstract machines inside a common definitional framework, this way being able to give sharp results about the relative time efficiencies. We also prove that non-idempotent intersection type theories are able to precisely reflect the time performances of the interactive abstract machine, this way showing that its time-inefficiency ultimately descends from the presence of higher-order types
Computability of differential equations
In this chapter, we provide a survey of results concerning the computability and computational complexity of differential equations. In particular, we study the conditions which ensure computability of the solution to an initial value problem for an ordinary differential equation (ODE) and analyze the computational complexity of a computable solution. We also present computability results concerning the asymptotic behaviors of ODEs as well as several classically important partial differential equations.info:eu-repo/semantics/acceptedVersio
Worst-Case Input Generation for Concurrent Programs under Non-Monotone Resource Metrics
Worst-case input generation aims to automatically generate inputs that
exhibit the worst-case performance of programs. It has several applications,
and can, for example, detect vulnerabilities to denial-of-service attacks.
However, it is non-trivial to generate worst-case inputs for concurrent
programs, particularly for resources like memory where the peak cost depends on
how processes are scheduled.
This article presents the first sound worst-case input generation algorithm
for concurrent programs under non-monotone resource metrics like memory. The
key insight is to leverage resource-annotated session types and symbolic
execution. Session types describe communication protocols on channels in
process calculi. Equipped with resource annotations, resource-annotated session
types not only encode cost bounds but also indicate how many resources can be
reused and transferred between processes. This information is critical for
identifying a worst-case execution path during symbolic execution. The
algorithm is sound: if it returns any input, it is guaranteed to be a valid
worst-case input. The algorithm is also relatively complete: as long as
resource-annotated session types are sufficiently expressive and the background
theory for SMT solving is decidable, a worst-case input is guaranteed to be
returned. A simple case study of a web server's memory usage demonstrates the
utility of the worst-case input generation algorithm
Slanted canonicity of analytic inductive inequalities
We prove an algebraic canonicity theorem for normal LE-logics of arbitrary
signature, in a generalized setting in which the non-lattice connectives are
interpreted as operations mapping tuples of elements of the given lattice to
closed or open elements of its canonical extension. Interestingly, the
syntactic shape of LE-inequalities which guarantees their canonicity in this
generalized setting turns out to coincide with the syntactic shape of analytic
inductive inequalities, which guarantees LE-inequalities to be equivalently
captured by analytic structural rules of a proper display calculus. We show
that this canonicity result connects and strengthens a number of recent
canonicity results in two different areas: subordination algebras, and transfer
results via G\"odel-McKinsey-Tarski translations.Comment: arXiv admin note: text overlap with arXiv:1603.08515,
arXiv:1603.0834