Compositional Satisfiability Solving in Separation Logic

We introduce a novel decision procedure to the satisfiability problem in array separation logic combined with general inductively defined predicates and arithmetic. Our proposal differentiates itself from existing works by solving satisfiability through compositional reasoning. First, following Fermat’s method of infinite descent, it infers for every inductive definition a “base” that precisely characterises the satisfiability. It then utilises the base to derive such a base for any formula where these inductive predicates reside in. Especially, we identify an expressive decidable fragment for the compositionality. We have implemented the proposal in a tool and evaluated it over challenging problems. The experimental results show that the compositional satisfiability solving is efficient and our tool is effective and efficient when compared with existing solvers

iTRAQ Identification of Candidate Serum Biomarkers Associated with Metastatic Progression of Human Prostate Cancer

A major challenge in the management of patients with prostate cancer is identifying those individuals at risk of developing metastatic disease, as in most cases the disease will remain indolent. We analyzed pooled serum samples from 4 groups of patients (n = 5 samples/group), collected prospectively and actively monitored for a minimum of 5 yrs. Patients groups were (i) histological diagnosis of benign prostatic hyperplasia with no evidence of cancer ‘BPH’, (ii) localised cancer with no evidence of progression, ‘non-progressing’ (iii) localised cancer with evidence of biochemical progression, ‘progressing’, and (iv) bone metastasis at presentation ‘metastatic’. Pooled samples were immuno-depleted of the 14 most highly abundant proteins and analysed using a 4-plex iTRAQ approach. Overall 122 proteins were identified and relatively quantified. Comparisons of progressing versus non-progressing groups identified the significant differential expression of 25 proteins (p<0.001). Comparisons of metastatic versus progressing groups identified the significant differential expression of 23 proteins. Mapping the differentially expressed proteins onto the prostate cancer progression pathway revealed the dysregulated expression of individual proteins, pairs of proteins and ‘panels’ of proteins to be associated with particular stages of disease development and progression. The median immunostaining intensity of eukaryotic translation elongation factor 1 alpha 1 (eEF1A1), one of the candidates identified, was significantly higher in osteoblasts in close proximity to metastatic tumour cells compared with osteoblasts in control bone (p = 0.0353, Mann Whitney U). Our proteomic approach has identified leads for potentially useful serum biomarkers associated with the metastatic progression of prostate cancer. The panels identified, including eEF1A1 warrant further investigation and validation

The Bernays-Schönfinkel-Ramsey Class of Separation Logic on Arbitrary Domains

International audienceThis paper investigates the satisfiability problem for Separation Logic with k record fields, with unrestricted nesting of separating conjunctions and implications , for prenex formulae with quantifier prefix ∃ * ∀ *. In analogy with first-order logic, we call this fragment Bernays-Schönfinkel-Ramsey Separation Logic [BSR(SL k)]. In contrast to existing work in Separation Logic, in which the universe of possible locations is assumed to be infinite, both finite and infinite universes are considered. We show that, unlike in first-order logic, the (in)finite sat-isfiability problem is undecidable for BSR(SL k). Then we define two non-trivial subsets thereof, that are decidable for finite and infinite satisfiability respectively, by controlling the occurrences of universally quantified variables within the scope of separating implications, as well as the polarity of the occurrences of the latter. Beside the theoretical interest, our work has natural applications in program verification, for checking that constraints on the shape of a data-structure are preserved by a sequence of transformations

A Decision Procedure for Separation Logic in SMT

International audienceThis paper presents a complete decision procedure for the entire quantifier-free fragment of Separation Logic (SL) interpreted over heaplets with data elements ranging over a parametric multi-sorted (possibly infinite) domain. The algorithm uses a combination of theories and is used as a specialized solver inside a DPLL(T) architecture. A prototype was implemented within the CVC4 SMT solver. Preliminary evaluation suggests the possibility of using this procedure as a building block of a more elaborate theorem prover for SL with inductive predicates , or as back-end of a bounded model checker for programs with low-level pointer and data manipulations

Reasoning in the Bernays-Schönfinkel-Ramsey Fragment of Separation Logic

Separation Logic (SL) is a well-known assertion language used in Hoare-style modular proof systems for programs with dynamically allocated data structures. In this paper we investigate the fragment of first-order SL restricted to the Bernays-Schoenfinkel-Ramsey quantifier prefix $\exists^*\forall^*$, where the quantified variables range over the set of memory locations. When this set is uninterpreted (has no associated theory) the fragment is PSPACE-complete, which matches the complexity of the quantifier-free fragment. However, SL becomes undecidable when the quantifier prefix belongs to $\exists^*\forall^*\exists^*$ instead, or when the memory locations are interpreted as integers with linear arithmetic constraints, thus setting a sharp boundary for decidability within SL. We have implemented a decision procedure for the decidable fragment of $\exists^*\forall^*$SL as a specialized solver inside a DPLL($T$) architecture, within the CVC4 SMT solver. The evaluation of our implementation was carried out using two sets of verification conditions, produced by (i) unfolding inductive predicates, and (ii) a weakest precondition-based verification condition generator. Experimental data shows that automated quantifier instantiation has little overhead, compared to manual model-based instantiation