565 research outputs found
ILP Modulo Data
The vast quantity of data generated and captured every day has led to a
pressing need for tools and processes to organize, analyze and interrelate this
data. Automated reasoning and optimization tools with inherent support for data
could enable advancements in a variety of contexts, from data-backed decision
making to data-intensive scientific research. To this end, we introduce a
decidable logic aimed at database analysis. Our logic extends quantifier-free
Linear Integer Arithmetic with operators from Relational Algebra, like
selection and cross product. We provide a scalable decision procedure that is
based on the BC(T) architecture for ILP Modulo Theories. Our decision procedure
makes use of database techniques. We also experimentally evaluate our approach,
and discuss potential applications.Comment: FMCAD 2014 final version plus proof
On the Convexity of a Fragment of Pure Set Theory with Applications within a Nelson-Oppen Framework
In Proceedings GandALF 2021, arXiv:2109.0779
Model Checking Parse Trees
Parse trees are fundamental syntactic structures in both computational
linguistics and compilers construction. We argue in this paper that, in both
fields, there are good incentives for model-checking sets of parse trees for
some word according to a context-free grammar. We put forward the adequacy of
propositional dynamic logic (PDL) on trees in these applications, and study as
a sanity check the complexity of the corresponding model-checking problem:
although complete for exponential time in the general case, we find natural
restrictions on grammars for our applications and establish complexities
ranging from nondeterministic polynomial time to polynomial space in the
relevant cases.Comment: 21 + x page
Decidability of E*A-sentences in Membership Theories
3The problem is addressed of establishing the satisfiability of prenex formulas involving a single universal quantifier, in diversified axiomatic set theories. A rather general decision method for solving this problem is illustrated through the treatment of membership theories of increasing strength, ending with a subtheory of Zermelo-Fraenkel which is already complete with respect to the There Exists*For All class of sentences. NP-hardness and NP-completeness results concerning the problems under study are achieved and a technique for restricting the universal quantifier is presented.opennoneopenOMODEO E.; PARLAMENTO F; POLICRITI A.Omodeo, E.; Parlamento, Franco; Policriti, Albert
Decidable Classes of Tree Automata Mixing Local and Global Constraints Modulo Flat Theories
We define a class of ranked tree automata TABG generalizing both the tree
automata with local tests between brothers of Bogaert and Tison (1992) and with
global equality and disequality constraints (TAGED) of Filiot et al. (2007).
TABG can test for equality and disequality modulo a given flat equational
theory between brother subterms and between subterms whose positions are
defined by the states reached during a computation. In particular, TABG can
check that all the subterms reaching a given state are distinct. This
constraint is related to monadic key constraints for XML documents, meaning
that every two distinct positions of a given type have different values. We
prove decidability of the emptiness problem for TABG. This solves, in
particular, the open question of the decidability of emptiness for TAGED. We
further extend our result by allowing global arithmetic constraints for
counting the number of occurrences of some state or the number of different
equivalence classes of subterms (modulo a given flat equational theory)
reaching some state during a computation. We also adapt the model to unranked
ordered terms. As a consequence of our results for TABG, we prove the
decidability of a fragment of the monadic second order logic on trees extended
with predicates for equality and disequality between subtrees, and cardinality.Comment: 39 pages, to appear in LMCS journa
Light On String Solving: Approaches to Efficiently and Correctly Solving String Constraints
Widespread use of string solvers in formal analysis of string-heavy programs has led to a growing demand for more efficient and reliable techniques which can be applied in this context, especially for real-world cases. Designing an algorithm for the (generally undecidable) satisfiability problem for systems of string constraints requires a thorough understanding of the structure of constraints present in the targeted cases. We target the aforementioned case in different perspectives: We present an algorithm which works by reformulating the satisfiability of bounded word equations as a reachability problem for non-deterministic finite automata. Secondly, we present a transformation-system-based technique to solving string constraints. Thirdly, we investigate benchmarks presented in the literature containing regular expression membership predicates and design a decission procedure for a PSPACE-complete sub-theory. Additionally, we introduce a new benchmarking framework for string solvers and use it to showcase the power of our algorithms via an extensive empirical evaluation over a diverse set of benchmarks
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