Model checking coalitional games in shortage resource scenarios

Verification of multi-agents systems (MAS) has been recently studied taking into account the need of expressing resource bounds. Several logics for specifying properties of MAS have been presented in quite a variety of scenarios with bounded resources. In this paper, we study a different formalism, called Priced Resource-Bounded Alternating-time Temporal Logic (PRBATL), whose main novelty consists in moving the notion of resources from a syntactic level (part of the formula) to a semantic one (part of the model). This allows us to track the evolution of the resource availability along the computations and provides us with a formalisms capable to model a number of real-world scenarios. Two relevant aspects are the notion of global availability of the resources on the market, that are shared by the agents, and the notion of price of resources, depending on their availability. In a previous work of ours, an initial step towards this new formalism was introduced, along with an EXPTIME algorithm for the model checking problem. In this paper we better analyze the features of the proposed formalism, also in comparison with previous approaches. The main technical contribution is the proof of the EXPTIME-hardness of the the model checking problem for PRBATL, based on a reduction from the acceptance problem for Linearly-Bounded Alternating Turing Machines. In particular, since the problem has multiple parameters, we show two fixed-parameter reductions.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Processing Succinct Matrices and Vectors

We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of a semiring (instead of 0 and 1). A simple example shows that the product of two MTDD-represented matrices cannot be represented by an MTDD of polynomial size. To overcome this deficiency, we extended MTDDs to MTDD_+ by allowing componentwise symbolic addition of variables (of the same dimension) in rules. It is shown that accessing an entry, equality checking, matrix multiplication, and other basic matrix operations can be solved in polynomial time for MTDD_+-represented matrices. On the other hand, testing whether the determinant of a MTDD-represented matrix vanishes PSPACE$-complete, and the same problem is NP-complete for MTDD_+-represented diagonal matrices. Computing a specific entry in a product of MTDD-represented matrices is #P-complete.Comment: An extended abstract of this paper will appear in the Proceedings of CSR 201

Two Variable vs. Linear Temporal Logic in Model Checking and Games

Model checking linear-time properties expressed in first-order logic has non-elementary complexity, and thus various restricted logical languages are employed. In this paper we consider two such restricted specification logics, linear temporal logic (LTL) and two-variable first-order logic (FO2). LTL is more expressive but FO2 can be more succinct, and hence it is not clear which should be easier to verify. We take a comprehensive look at the issue, giving a comparison of verification problems for FO2, LTL, and various sublogics thereof across a wide range of models. In particular, we look at unary temporal logic (UTL), a subset of LTL that is expressively equivalent to FO2; we also consider the stutter-free fragment of FO2, obtained by omitting the successor relation, and the expressively equivalent fragment of UTL, obtained by omitting the next and previous connectives. We give three logic-to-automata translations which can be used to give upper bounds for FO2 and UTL and various sublogics. We apply these to get new bounds for both non-deterministic systems (hierarchical and recursive state machines, games) and for probabilistic systems (Markov chains, recursive Markov chains, and Markov decision processes). We couple these with matching lower-bound arguments. Next, we look at combining FO2 verification techniques with those for LTL. We present here a language that subsumes both FO2 and LTL, and inherits the model checking properties of both languages. Our results give both a unified approach to understanding the behaviour of FO2 and LTL, along with a nearly comprehensive picture of the complexity of verification for these logics and their sublogics.Comment: 37 pages, to be published in Logical Methods in Computer Science journal, includes material presented in Concur 2011 and QEST 2012 extended abstract

First-Order and Temporal Logics for Nested Words

Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We provide new temporal logics for finite and infinite nested words, which are natural extensions of LTL, and prove that these logics are first-order expressively-complete. One of them is based on adding a "within" modality, evaluating a formula on a subword, to a logic CaRet previously studied in the context of verifying properties of recursive state machines (RSMs). The other logic, NWTL, is based on the notion of a summary path that uses both the linear and nesting structures. For NWTL we show that satisfiability is EXPTIME-complete, and that model-checking can be done in time polynomial in the size of the RSM model and exponential in the size of the NWTL formula (and is also EXPTIME-complete). Finally, we prove that first-order logic over nested words has the three-variable property, and we present a temporal logic for nested words which is complete for the two-variable fragment of first-order.Comment: revised and corrected version of Mar 03, 201

Learning Effective Changes for Software Projects

The primary motivation of much of software analytics is decision making. How to make these decisions? Should one make decisions based on lessons that arise from within a particular project? Or should one generate these decisions from across multiple projects? This work is an attempt to answer these questions. Our work was motivated by a realization that much of the current generation software analytics tools focus primarily on prediction. Indeed prediction is a useful task, but it is usually followed by "planning" about what actions need to be taken. This research seeks to address the planning task by seeking methods that support actionable analytics that offer clear guidance on what to do. Specifically, we propose XTREE and BELLTREE algorithms for generating a set of actionable plans within and across projects. Each of these plans, if followed will improve the quality of the software project.Comment: 4 pages, 2 figures. This a submission for ASE 2017 Doctoral Symposiu

AbsSynthe: abstract synthesis from succinct safety specifications

In this paper, we describe a synthesis algorithm for safety specifications described as circuits. Our algorithm is based on fixpoint computations, abstraction and refinement, it uses binary decision diagrams as symbolic data structure. We evaluate our tool on the benchmarks provided by the organizers of the synthesis competition organized within the SYNT'14 workshop.Comment: In Proceedings SYNT 2014, arXiv:1407.493