22 research outputs found
Internal Calculi for Separation Logics
We present a general approach to axiomatise separation logics with heaplet semantics with no external features such as nominals/labels. To start with, we design the first (internal) Hilbert-style axiomatisation for the quantifier-free separation logic SL(?, -*). We instantiate the method by introducing a new separation logic with essential features: it is equipped with the separating conjunction, the predicate ls, and a natural guarded form of first-order quantification. We apply our approach for its axiomatisation. As a by-product of our method, we also establish the exact expressive power of this new logic and we show PSpace-completeness of its satisfiability problem
Extending Propositional Separation Logic for Robustness Properties
We study an extension of propositional separation logic that can specify robustness properties, such as acyclicity and garbage freedom, for automatic verification of stateful programs with singly-linked lists. We show that its satisfiability problem is PSpace-complete, whereas modest extensions of the logic are shown to be Tower-hard. As separating implication, reachability predicates (under some syntactical restrictions) and a unique quantified variable are allowed, this logic subsumes several PSpace-complete separation logics considered in previous works
Distributed execution of bigraphical reactive systems
The bigraph embedding problem is crucial for many results and tools about
bigraphs and bigraphical reactive systems (BRS). Current algorithms for
computing bigraphical embeddings are centralized, i.e. designed to run locally
with a complete view of the guest and host bigraphs. In order to deal with
large bigraphs, and to parallelize reactions, we present a decentralized
algorithm, which distributes both state and computation over several concurrent
processes. This allows for distributed, parallel simulations where
non-interfering reactions can be carried out concurrently; nevertheless, even
in the worst case the complexity of this distributed algorithm is no worse than
that of a centralized algorithm
On Deciding Linear Arithmetic Constraints Over p-adic Integers for All Primes
Given an existential formula Φ of linear arithmetic over p-adic integers together with valuation constraints, we study the p-universality problem which consists of deciding whether Φ is satisfiable for all primes p, and the analogous problem for the closely related existential theory of Büchi arithmetic. Our main result is a coNEXP upper bound for both problems, together with a matching
lower bound for existential BĂĽchi arithmetic. On a technical level, our results are obtained from analysing properties of a certain class of p-automata, finite-state automata whose languages encode
sets of tuples of natural numbers
Axiomatising logics with separating conjunctions and modalities
International audienceModal separation logics are formalisms that combine modal operators to reason locally, with separating connectives that allow to perform global updates on the models. In this work, we design Hilbert-style proof systems for the modal separation logics MSL(⇤, h6 =i) and MSL(⇤, 3), where ⇤ is the separating conjunction, 3 is the standard modal operator and h6 =i is the di↵erence modality. The calculi only use the logical languages at hand (no external features such as labels) and take advantage of new normal forms and of their axiomatisation
Towards distributed bigraphical reactive systems
3noThe bigraph embedding problem is crucial for many results and tools about bigraphs and bigraphical reactive systems (BRS). There are algorithms for computing bigraphical embedding but these are designed to be run locally and assume a complete view of the guest and host bigraphs, putting large bigraphs and BRS out of their reach. To overcome these limitations we present a decentralized algorithm for computing bigraph embeddings that allows us to distribute both state and computation over several concurrent processes. Among various applications, this algorithm offers the basis for distributed BRS simulations where non-interfering reactions are carried out concurrently.openopenMansutti, Alessio; Peressotti, Marco; Miculan, MarinoMansutti, Alessio; Peressotti, Marco; Miculan, Marin
On Polynomial-Time Decidability of k-Negations Fragments of FO Theories (Extended Abstract)
This paper introduces a generic framework that provides sufficient conditions for guaranteeing polynomial-time decidability of fixed-negation fragments of first-order theories that adhere to certain fixed-parameter tractability requirements. It enables deciding sentences of such theories with arbitrary existential quantification, conjunction and a fixed number of negation symbols in polynomial time. It was recently shown by Nguyen and Pak [SIAM J. Comput. 51(2): 1-31 (2022)] that an even more restricted such fragment of Presburger arithmetic (the first-order theory of the integers with addition and order) is NP-hard. In contrast, by application of our framework, we show that the fixed negation fragment of weak Presburger arithmetic, which drops the order relation from Presburger arithmetic in favour of equality, is decidable in polynomial time
A Complete Axiomatisation for Quantifier-Free Separation Logic
We present the first complete axiomatisation for quantifier-free separation
logic. The logic is equipped with the standard concrete heaplet semantics and
the proof system has no external feature such as nominals/labels. It is not
possible to rely completely on proof systems for Boolean BI as the concrete
semantics needs to be taken into account. Therefore, we present the first
internal Hilbert-style axiomatisation for quantifier-free separation logic. The
calculus is divided in three parts: the axiomatisation of core formulae where
Boolean combinations of core formulae capture the expressivity of the whole
logic, axioms and inference rules to simulate a bottom-up elimination of
separating connectives, and finally structural axioms and inference rules from
propositional calculus and Boolean BI with the magic wand