# Questions tagged [smt-solvers]

Solver programs for the Satisfiability Modulo Theories (SMT). The SMT problem is a decision problem for logical formulas with combinations of background theories expressed in classical first-order logic with equality.

37 questions
Filter by
Sorted by
Tagged with
16 views

### How overapproximation of boolean abstraction function works?

I just found that if original formula is unsat, using boolean abstraction function can result in sat. Clearly this is overapproximate. I wonder if I have contingent formula, does that means my boolean ...
29 views

### Specific quantifier elimination for real algebraic numbers

It is well-known that the theory of (first-order) real arithmetic, $\mathcal{T}_{\mathbb{R}}$, is decidable, both on its linear and non-linear (a.k.a field) fragments, since Tarski-Seindenberg proved ...
53 views

In the question (Validity of predicate logic formulas) I see the following way of expressing: "The predicate $P(x,y) \equiv \bigl[ y \cdot x = 1 \bigr]$, where the domain of discourse is $\... 1 vote 0 answers 50 views ### SMT validity solvers/ quantifier elimination in Ocaml I am working on my own expression package in Ocaml and have to perform both validity queries and quantifier elimination. I have already implemented Cooper's procedure (for Presburger and Linear ... 1 vote 1 answer 86 views ### Are there any solvers that can handle non-linearity? I need a way to solve linear and non-linear inequalities over the natural numbers. So equations like this should be solveable:$\forall n, p, q \in \mathbb{N}. q \cdot (1 + n^p) \leq q$From what I ... 2 votes 1 answer 46 views ### How to represent bottom element (integer domains) in SMT formula I'm doing some work with static analysis and need to represent local variables as SMT formulas. In general this is fairly straight forward, depending on the domain of the static analysis. However, ... 0 votes 0 answers 23 views ### SAT solvers that can compute prime implicants and/or minimization I'm looking into computing the prime implicants of a Boolean function. I have found many different algorithms in the literature, many of them relying on SAT solvers. However, I have not been able to ... 3 votes 0 answers 26 views ### Polymorphism in SMT solvers What are the theoretical limitations that avoid the adoption of type polymorphism à la System F in current SMT solvers? I work in the context of program verification and I am surprised by the great ... 1 vote 1 answer 62 views ### Assign few binary variables to make all polynomials identically zero I have 50 polynomials$f_i$over binary variables$(x_1,\ldots,x_{100})$. Also$f_i(0,0,\ldots,0)=0$for any$i \in [1,50]$. I want to assign few variables so that all$f_i$will be identically zero. ... 0 votes 2 answers 52 views ### Tutorials/resources for building a toy SMT solver I've built a rudimentary SAT Solver from scratch, and wanted to do the same with SMT solvers as well. While I've found two toy SMT Solver implementations in Haskell and Ocaml, but no tutorials or ... 0 votes 1 answer 35 views ### Which of these properties hold for all FO theories? (but not regarding fragments thereof) Which of these properties hold for all FO theories? (but not regarding fragments thereof) a. Decidable b. At least expressive as propositional logic c. NP-complete a) Decidable: no, some first order ... 2 votes 2 answers 86 views ### Constraint satisfaction problem: solve system, then evaluate whether many additional constraints are satisfied one at a time I have a system that consists of binary inequality constraints between variables, plus some indicator variables that can assume only two values: ... 1 vote 2 answers 202 views ### Automated reasoning with real numbers I have a large number of equivalences which look like:$(a \leq 0.54 \wedge b \geq 0.12) \vee (c \gt 0.98)\Leftrightarrow(x \leq 0.25) \vee (x \gt 0.91 \wedge y \geq 0.01)$This is just an ... 3 votes 1 answer 45 views ### How to leverage the fact that I'm solving 1000's of very similar SMT instances? I have a core SMT solver problem consisting of 100,000 bit-vector array clauses, and one 10000-dimensional bit-vector array. Then, my program takes as input k << 100,000 new clauses, and adds ... 0 votes 1 answer 342 views ### What are the differences between symbolic execution and SAT solvers? My understanding is that symbolic execution only deals with specific paths and bad patterns, while SAT solvers, or satisfiability modulo theories in general, provide a much more robust analysis of the ... 2 votes 1 answer 37 views ### Proving that a property is k-inductive with an SMT solver (parametric resettable counter) I'm following the slides at https://homepage.cs.uiowa.edu/~tinelli/talks/FT-11.pdf where Tinelli explains how k-induction works in the context of SMT based model checking. A parametric and resettable ... 0 votes 0 answers 52 views ### Program synthesis based on function properties I am fairly new at program synthesis and the use of SMT solvers for this purpose. Given a function g, I want to generate all the functions f and h such that the following holds: f . g = h . f Are ... 4 votes 1 answer 325 views ### Check if two items are equal after replacing Let's say that an item is either a natural number or a list of items. Examples of items are: 1  [4, [3, 1], 3, 4] A rule states that two items are equal. For example: 1 = 2 3 = [3, 1] [4, 3] = [... 0 votes 1 answer 21 views ### Generating graph with complex structure I want to generate a bunch of graphs of about 100 nodes, where each node is a categorial variable. I want the graphs to satisfy complex properties, like, "if a node of type A is connected to a node ... 1 vote 0 answers 147 views ### General Understanding of SMT Solving Across Multiple Theories My first question was a little too simplified in that it turned out to be an integer linear programming problem solvable with the Simplex Method. However, what I think I am wondering about is how to ... -2 votes 1 answer 250 views ### How a SMT / SAT Solver Generates Valuations for this Example First, an example of a set of constraints which turned out not to be solvable (I don't think): ... 2 votes 0 answers 152 views ### Passing arrays vs functions as arguments in SMT? In SAT Modulo Theories (SMT), with the theory of uninterpreted functions, all functions are first order, that is, they don't take functions as arguments or return functions. In the theory of arrays, ... 0 votes 1 answer 80 views ### Objective function and constraint satisfaction over a set of multi-attributes elements I'm looking for an approach to solve a problem consisting of maximizing an objective function over a set of discrete elements, while respecting a set of constraints. To illustrate my point, I'll try ... 2 votes 1 answer 2k views ### Bit Blasting Algorithm I found a pseudo algorithm which describes bit blasting: click (page 156,157). I am trying to implement it in C, but I don't understand it yet completely. Let's make an example: Assume our bit-vectors ... 4 votes 2 answers 1k views ### How could an SMT solver be implemented as simple as possible? I'm trying to figure out how an SMT solver works as simple as possible. Let's assume we have a simple input program with symbolic values x and ... 0 votes 0 answers 152 views ### When to use SAT vs solving? Are there any guidelines for how to recognize, for a given problem, which approach is more likely to yield good results? SAT solver or SMT solver? Is there any guidance anyone can offer about which ... 0 votes 1 answer 57 views ### Verification condition in case of array theory As far as i can understand the problem of checking safety property, can be reduce to solving for inductive invariants in VC's and there is following parts to it: Generate VC's from the program. Solve ... 3 votes 3 answers 188 views ### Is the optimal order of graph vertices s.t. minimizes edges to later vertices a well-known problem? I'm a little unfamiliar with graph theory, and I found an interesting problem in my work that I do not know if its already well-known or can be easily mapped to another one. If I were to express the ... 4 votes 0 answers 51 views ### How the$EX(f)\$ is evaluated in symbolic model checking?

I was reading the symbolic model checking, So there it has mentioned that we can represent the set of states and transition relations of any transition system with the help of ROBDDs. I was trying to ...
248 views

### Framework or tools to generate theorem prover/solver/reasoner for new logic

I have new logic which has syntax and semantics in usual natural languages and I have to create theorem prover/solver/reasoner for this logic. Is there framework or tool set that can generate such ...
1 vote
200 views

### Using SMT Solvers in formula checking

I'm currently working on a static analysis work in which I need to check whether a given formula is met or not. I hope the following example clarifies my requirement. Suppose we have a list of three-...
678 views

### Exponential example for simplex used in SMT solvers

The original simplex algorithm requires an exponential number of pivot operations in the worst case, e.g., if run on the Klee-Minty example [3,4]. What about the simplex algorithm used in SMT solvers ...
49 views

So this sounds like this might lead to an undecidable theory but I thought I would give it a try and ask about it after I found nothing on the subject. I am somewhat interested in finding functions ...
342 views

### Using SMT solvers to generate random solutions to given predicate

I am interested in generating random solutions to predicates. I only need SMT for integers with the following predicates/functions <, >, <=, >=, ==, !=, +, * The algorithm I want should produce ...
176 views

### Introduction to bounded model checking that describes model generation

Most of the tutorials I have found on model checking and bounded model checking start with, the model is given as a Kripke Structure M = (S,I,T,L) where S is a set of states, I is a set of initial ...