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Despite the impressive quality improvements yielded by neural machine translation (NMT) systems, controlling their translation output to adhere to user-provided terminology constraints remains an open problem. We describe our approach to…
We consider the problem of solving floating-point constraints obtained from software verification. We present UppSAT --- a new implementation of a systematic approximation refinement framework [ZWR17] as an abstract SMT solver. Provided…
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
First-order linear real arithmetic enriched with uninterpreted predicate symbols yields an interesting modeling language. However, satisfiability of such formulas is undecidable, even if we restrict the uninterpreted predicate symbols to…
Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive…
This paper introduces a novel technique to decide the satisfiability of formulae written in the language of Linear Temporal Logic with Both future and past operators and atomic formulae belonging to constraint system D (CLTLB(D) for short).…
In many real world applications of machine learning, models have to meet certain domain-based requirements that can be expressed as constraints (e.g., safety-critical constraints in autonomous driving systems). Such constraints are often…
Solving constraints involving inductive (aka recursive) definitions is challenging. State-of-the-art SMT/CHC solvers and first-order logic provers provide only limited support for solving such constraints, especially when they involve,…
Mathematical optimization is ubiquitous in modern applications. However, in practice, we often need to use nonlinear optimization models, for which the existing optimization tools such as Cplex or Gurobi may not be directly applicable and…
We address the satisfiability problem for string constraints that combine relational constraints represented by transducers, word equations, and string length constraints. This problem is undecidable in general. Therefore, we propose a new…
Many constraint satisfaction problems involve synthesizing subgraphs that satisfy certain reachability constraints. This paper presents programs in Picat for four problems selected from the recent LP/CP programming competitions. The…
In the contexts of automated reasoning and formal verification, important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories…
We study a new extension of the weak MSO logic, talking about boundedness. Instead of a previously considered quantifier U, expressing the fact that there exist arbitrarily large finite sets satisfying a given property, we consider a…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…
When solving combinatorial problems, pruning symmetric solution candidates from the search space is essential. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints…
Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for solving NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
The study of word equations (or the existential theory of equations over free monoids) is a central topic in mathematics and theoretical computer science. The problem of deciding whether a given word equation has a solution was shown to be…
Given a compact basic semi-algebraic set $K\subset R^n\times R^m$, a simple set $B$ (box or ellipsoid), and some semi-algebraic function $f$, we consider sets defined with quantifiers, of the form $R_f:=\{x\in B: \mbox{$f(x,y)\leq 0$ for…
Constrained clustering has been well-studied for algorithms such as $K$-means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode…