Related papers: SMT Solving over Finite Field Arithmetic
Analysis of cryptographic protocols in a symbolic model is relative to a deduction system that models the possible actions of an attacker regarding an execution of this protocol. We present in this paper a transformation algorithm for such…
This paper presents algorithms for solving multiobjective integer programming problems. The algorithm uses Barvinok's rational functions of the polytope that defines the feasible region and provides as output the entire set of nondominated…
In this article, we provide a new algorithm for solving constraint satisfaction problems over templates with few subpowers, by reducing the problem to the combination of solvability of a polynomial number of systems of linear equations over…
The polynomial $x^n+1$ over finite fields has been of interest due to its applications in the study of negacyclic codes over finite fields. In this paper, a rigorous treatment of the factorization of $x^n+1$ over finite fields is given as…
The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance.…
We present a method for computing stable models of normal logic programs, i.e., logic programs extended with negation, in the presence of predicates with arbitrary terms. Such programs need not have a finite grounding, so traditional…
In this paper we present a satisfiability-preserving reduction from MITL interpreted over finitely-variable continuous behaviors to Constraint LTL over clocks, a variant of CLTL that is decidable, and for which an SMT-based bounded…
The theory of uninterpreted functions is a key modeling tool for systems with unknown or abstracted components. Some domains such as systems biology impose further restrictions regarding monotonicity on these components, requiring specific…
This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum…
Solving systems of m multivariate quadratic equations in n variables (MQ-problem) over finite fields is NP-hard. The security of many cryptographic systems is based on this problem. Up to now, the best algorithm for solving the underdefined…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
In this paper, we consider the problem of minimizing a smooth function, given as finite sum of black-box functions, over a convex set. In order to advantageously exploit the structure of the problem, for instance when the terms of the…
We present a novel idea to compute square roots over finite fields, without being given any quadratic nonresidue, and without assuming any unproven hypothesis. The algorithm is deterministic and the proof is elementary. In some cases, the…
We present a CLP(FD)-based constraint solver able to deal with unbounded domains. It is based on constraint propagation, resorting to enumeration if all other methods fail. An important aspect is detecting when enumeration was complete and…
In this paper we introduce a multistep generalization of the guess-and-determine or hybrid strategy for solving a system of multivariate polynomial equations over a finite field. In particular, we propose performing the exhaustive…
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…
This paper presents a complete decision procedure for the entire quantifier-free fragment of Separation Logic ($\seplog$) interpreted over heaplets with data elements ranging over a parametric multi-sorted (possibly infinite) domain. The…
Whether the satisfiability of any formula F of propositional calculus can be determined in polynomial time is an open question. I propose a simple procedure based on some real world mechanisms to tackle this problem. The main result is the…
This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as…
Local search has recently been applied to SMT problems over various arithmetic theories. Among these, nonlinear real arithmetic poses special challenges due to its uncountable solution space and potential need to solve higher-degree…