arXiv subjects
Publications and source records attributed to Mircea Marin.
The Working Formal Methods Symposium (FROM) is a series of workshops that aim to bring together researchers and practitioners who work on formal methods by contributing new theoretical results, methods, techniques, and frameworks, and/or by creating or using software tools that apply theoretical contributions.
We address the problem of enumerating all maximal clique-partitions of an undirected graph and present an algorithm based on the observation that every maximal clique-partition can be produced from the maximal clique-cover of the graph by assigning the vertices shared among maximal cliques, to belong to only one clique. This simple algorithm has the following drawbacks: (1) the search space is very large; (2) it finds some clique-partitions which are not maximal; and (3) some clique-partitions are found more than once. We propose two criteria to avoid these drawbacks. The outcome is an algorithm that explores a much smaller search space and guarantees that every maximal clique-partition is computed only once. The algorithm can be used in problems such as anti-unification with proximity relations or in resource allocation tasks when one looks for several alternative ways to allocate resources.
We study the matching problem of regular tree languages, that is, "$\exists σ:σ(L)\subseteq R$?" where $L,R$ are regular tree languages over the union of finite ranked alphabets $Σ$ and $\mathcal{X}$ where $\mathcal{X}$ is an alphabet of variables and $σ$ is a substitution such that $σ(x)$ is a set of trees in $T(Σ\cup H)\setminus H$ for all $x\in \mathcal{X}$. Here, $H$ denotes a set of "holes" which are used to define a "sorted" concatenation of trees. Conway studied this problem in the special case for languages of finite words in his classical textbook "Regular algebra and finite machines" published in 1971. He showed that if $L$ and $R$ are regular, then the problem "$\exists σ\forall x\in \mathcal{X}: σ(x)\neq \emptyset\wedge σ(L)\subseteq R$?" is decidable. Moreover, there are only finitely many maximal solutions, the maximal solutions are regular substitutions, and they are effectively computable. We extend Conway's results when $L,R$ are regular languages of finite and infinite trees, and language substitution is applied inside-out, in the sense of Engelfriet and Schmidt (1977/78). More precisely, we show that if $L\subseteq T(Σ\cup\mathcal{X})$ and $R\subseteq T(Σ)$ are regular tree languages over finite or infinite trees, then the problem "$\exists σ\forall x\in \mathcal{X}: σ(x)\neq \emptyset\wedge σ_{\mathrm{io}}(L)\subseteq R$?" is decidable. Here, the subscript "$\mathrm{io}$" in $σ_{\mathrm{io}}(L)$ refers to "inside-out". Moreover, there are only finitely many maximal solutions $σ$, the maximal solutions are regular substitutions and effectively computable. The corresponding question for the outside-in extension $σ_{\mathrm{oi}}$ remains open, even in the restricted setting of finite trees.
We analyze the expected running time of WalkSAT, a well-known local search procedure for satisfiability solving, on satisfiable instances of the k-XOR SAT problem. We obtain estimates of this expected running time by reducing the problem to a setting amenable to classical techniques from drift analysis. A crucial ingredient of this reduction is the definition of (new, explosive) hypergraph versions of interacting particle systems, notably of coalescing and annihilating random walks as well as the voter model. The use of these tools allows to show that the expected running time of WalkSAT depends on structural parameter (we call odd Cheeger drift) of the dual of the formula hypergraph.
This volume contains the proceedings of FROM 2019: the Third Symposium on Working Formal Methods, held on September 3-5, 2019 in Timişoara (Romania). FROM aims to bring together researchers and practitioners who work on formal methods by contributing new theoretical results, methods, techniques, and frameworks, and/or make the formal methods to work by creating or using software tools that apply theoretical contributions.
CLP(H) is an instantiation of the general constraint logic programming scheme with the constraint domain of hedges. Hedges are finite sequences of unranked terms, built over variadic function symbols and three kinds of variables: for terms, for hedges, and for function symbols. Constraints involve equations between unranked terms and atoms for regular hedge language membership. We study algebraic semantics of CLP(H) programs, define a sound, terminating, and incomplete constraint solver, investigate two fragments of constraints for which the solver returns a complete set of solutions, and describe classes of programs that generate such constraints.
We consider the problem of learning an unknown context-free grammar when the only knowledge available and of interest to the learner is about its structural descriptions with depth at most $\ell.$ The goal is to learn a cover context-free grammar (CCFG) with respect to $\ell$, that is, a CFG whose structural descriptions with depth at most $\ell$ agree with those of the unknown CFG. We propose an algorithm, called $LA^\ell$, that efficiently learns a CCFG using two types of queries: structural equivalence and structural membership. We show that $LA^\ell$ runs in time polynomial in the number of states of a minimal deterministic finite cover tree automaton (DCTA) with respect to $\ell$. This number is often much smaller than the number of states of a minimum deterministic finite tree automaton for the structural descriptions of the unknown grammar.
PRholog is an experimental extension of logic programming with strategic conditional transformation rules, combining Prolog with Rholog calculus. The rules perform nondeterministic transformations on hedges. Queries may have several results that can be explored on backtracking. Strategies provide a control on rule applications in a declarative way. With strategy combinators, the user can construct more complex strategies from simpler ones. Matching with four different kinds of variables provides a flexible mechanism of selecting (sub)terms during execution. We give an overview on programming with strategies in PRholog and demonstrate how rewriting strategies can be expressed.