Efficient First-Order Temporal Logic for Infinite-State Systems

In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for this form of specification and tractable enough for practical deductive verification. Importantly, the power of the temporal language allows us to describe (and verify) asynchronous systems, communication delays and more complex properties such as liveness and fairness properties. These aspects appear difficult for many other approaches to infinite-state verification.Comment: 16 pages, 2 figure

Data Querying with Ciphertext Policy Attribute Based Encryption

Data encryption limits the power and efficiency of queries. Direct processing of encrypted data should ideally be possible to avoid the need for data decryption, processing, and re-encryption. It is vital to keep the data searchable and sortable. That is, some information is intentionally leaked. This intentional leakage technology is known as "querying over encrypted data schemes", which offer confidentiality as well as querying over encrypted data, but it is not meant to provide flexible access control. This paper suggests the use of Ciphertext Policy Attributes Based Encryption (CP-ABE) to address three security requirements, namely: confidentiality, queries over encrypted data, and flexible access control. By combining flexible access control and data confidentiality, CP-ABE can authenticate who can access data and possess the secret key. Thus, this paper identifies how much data leakage there is in order to figure out what kinds of operations are allowed when data is encrypted by CP-ABE

A Model for Learning Description Logic Ontologies Based on Exact Learning

We investigate the problem of learning description logic (DL) ontologies in Angluin et al.’s framework of exact learning via queries posed to an oracle. We consider membership queries of the form “is a tuple a of individuals a certain answer to a data retrieval query q in a given ABox and the unknown target ontology?” and completeness queries of the form “does a hypothesis ontology entail the unknown target ontology?” Given a DL L and a data retrieval query language Q, we study polynomial learnability of ontologies in L using data retrieval queries in Q and provide an almost complete classification for DLs that are fragments of EL with role inclusions and of DL-Lite and for data retrieval queries that range from atomic queries and EL/ELI-instance queries to conjunctive queries. Some results are proved by non-trivial reductions to learning from subsumption examples

Practical First-Order Temporal Reasoning

In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for this form of specification and tractable enough for practical deductive verification. Importantly, the power of the temporal language allows us to describe (and verify) asynchronous systems, communication delays and more complex liveness and fairness properties. These aspects appear difficult for many other approaches to infinite-state verification. 1

Computer-aided proof of Erdős discrepancy properties

In 1930s Paul Erdős conjectured that for any positive integer C in any infinite ±1 sequence (xn) there exists a subsequence xd, x2d, x3d, ..., xkd, for some positive integers k and d, such that |∑ki=1xi·d| >C. The conjecture has been referred to as one of the major open problems in combinatorial number theory and discrepancy theory. For the particular case of C = 1 a human proof of the conjecture exists; for C = 2 a bespoke computer program had generated sequences of length 1124 of discrepancy 2, but the status of the conjecture remained open even for such a small bound. We show that by encoding the problem into Boolean satisfiability and applying the state of the art SAT solvers, one can obtain a discrepancy 2 sequence of length 1160 and a proof of the Erdős discrepancy conjecture for C = 2, claiming that no discrepancy 2 sequence of length 1161, or more, exists. In the similar way, we obtain a precise bound of 127 645 on the maximal lengths of both multiplicative and completely multiplicative sequences of discrepancy 3. We also demonstrate that unrestricted discrepancy 3 sequences can be longer than 130 000